Journal articles on the topic 'Residual maximum likelihood method (REML)'
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Clarke, Robin T. "Residual maximum likelihood (REML) methods for analysing hydrological data series." Journal of Hydrology 182, no. 1-4 (July 1996): 277–95. http://dx.doi.org/10.1016/0022-1694(95)02929-x.
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Noerwijati, Kartika, NFn Nasrullah, NFn Taryono, and Djoko Prajitno. "ANALISIS GGE BIPLOT PADA HASIL KLON-KLON UBI KAYU MENGGUNAKAN METODE RESTRICTED MAXIMUM LIKELIHOOD." Informatika Pertanian 25, no. 1 (June 3, 2016): 89. http://dx.doi.org/10.21082/ip.v25n1.2016.p89-98.
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The study was conducted in five locations i.e Kediri, Ponorogo, Probolinggo, Malang, and Mojokerto, from November 2010 until August 2011. The planting materials used were 15 cassava clones. The research objective was to compare analysis methods of the genotype × environment interaction, namely: a) GGE technique using REML without A matrix by assuming homogeneous residual error variance, b) GGE technique using REML with A matrix by assuming homogeneous residual error variance, c) GGE technique using REML without A matrix by assuming heterogeneous residual error variance, and d) GGE technique using REML with A matrix by assuming heterogeneous residual error variance. The results showed that GGE technique using REML without A matrix by assuming heterogeneous residual error variance was more appropriate. Clones CMM 03038-7 (G8) had a wide adaptability and high yield potential, and its clone was closest to the ideal criteria for genotype compared with other genotypes. Clones CMM 03094-4 (G10) had specific adaptability in the environments S2 (Malang) and S5 (Mojokerto), and it had higher yield potential than the control varieties UJ5, Malang 6, and Adira 4. Environment Kediri (S1) had the highest yield among other environments and Kediri was a suitable environment for the growth and selection of cassava.<p align="center"> </p>
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Ben Zaabza, Hafedh, Abderrahmen Ben Gara, Hedi Hammami, Mohamed Amine Ferchichi, and Boulbaba Rekik. "Estimation of variance components of milk, fat, and protein yields of Tunisian Holstein dairy cattle using Bayesian and REML methods." Archives Animal Breeding 59, no. 2 (June 1, 2016): 243–48. http://dx.doi.org/10.5194/aab-59-243-2016.
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Abstract. A multi-trait repeatability animal model under restricted maximum likelihood (REML) and Bayesian methods was used to estimate genetic parameters of milk, fat, and protein yields in Tunisian Holstein cows. The estimates of heritability for milk, fat, and protein yields from the REML procedure were 0.21 ± 0.05, 0.159 ± 0.04, and 0.158 ± 0.04, respectively. The corresponding results from the Bayesian procedure were 0.273 ± 0.02, 0.198 ± 0.01, and 0.187 ± 0.01. Heritability estimates tended to be larger via the Bayesian than those obtained by the REML method. Genetic and permanent environmental variances estimated by REML were smaller than those obtained by the Bayesian analysis. Inversely, REML estimates of the residual variances were larger than Bayesian estimates. Genetic and permanent correlation estimates were on the other hand comparable by both REML and Bayesian methods with permanent environmental being larger than genetic correlations. Results from this study confirm previous reports on genetic parameters for milk traits in Tunisian Holsteins and suggest that a multi-trait approach can be an alternative for implementing a routine genetic evaluation of the Tunisian dairy cattle population.
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Lill, W. J., A. C. Gleeson, and B. R. Cullis. "Relative accuracy of a neighbour method for field trials." Journal of Agricultural Science 111, no. 2 (October 1988): 339–46. http://dx.doi.org/10.1017/s0021859600083283.
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SummaryTwo scries of simulation experiments were used to investigate the accuracy of treatment and variance estimation with a neighbour analysis of field trials proposed by Gleeson & Cullis (1987). The first series examined the accuracy of residual maximum likelihood (REML) estimation of seven theoretical error models applicable to field trials. REML estimation provided accurate estimates of the variance parameters, but the Ftest of treatments was slightly biased upward (to +2·4%) for first differences models and slightly biased downwards (to –1·4%) for second differences models. The second series of simulations, based on 19 uniformity data sets, illustrated that treatment effects were consistently estimated more accurately by the REML neighbour (RN) analysis of Gleeson & Cullis (1987) than by incomplete block (IB) analysis with recovery of interblock information. The relative gain in accuracy of RN over IB depends on the amount of systematic variation or ‘trend’ in the trial, and ranged from 6 to 18% with an average of 12% for a range of trend and error variances commonly encountered in field trials. The predicted average standard errors of pairwise treatment differences from the RN analysis were in close agreement with their empirical estimates, indicating that the predicted average S.E.D. is approximately valid.
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Candido, Willame dos Santos, Caique Machado e. Silva, Maraiza Lima Costa, Bruna Elaine de Almeida Silva, Pedro Henrique Sousa Almeida, Igor Ferreira Coelho, and Edésio Fialho dos Reis. "Selection of top cross hybrids for green maize yield via REML/Blup method." January 2020, no. 14(01) 2020 (January 20, 2020): 172–78. http://dx.doi.org/10.21475/ajcs.20.14.01.p2061.
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The purpose of this study was to select top cross hybrids of green maize for yield, derived from partially inbred S1 lines based on genetic values using the REML/Blup method, and to estimate important genetic parameters for green maize breeding programs. The experiment was conducted in an experimental area located between 17º53´ S and 52º43´ W, 680 m altitude. The evaluation of 75 top cross hybrids was performed in a randomized block design with four replicates. A sample of five plants/ears was used in each plot to evaluate grain mass trait (MASS). For commercial ear yield trait (CEYIELD), evaluations were carried out for the total number of plants per plot. Hybrids were selected via BLUP procedures using the Selegen-REML/Blup program. Based on the Restricted Maximum Likelihood (REML), we estimated the coefficients of genetic and residual variation and components of variance, by which a genetic variability between the top cross hybrids was observed. This shows the possibility of successful selection for the traits under evaluation. The estimated accuracy for the selection of top cross hybrids was 0.81 for commercial ear yield and 0.64 for grain mass, pointing to high and moderate precision levels for CEYIELD and MASS traits, respectively, corroborating the possibility of success in selecting top cross hybrids based on the CEYIELD trait. The predicted genetic gain from the selection was 20.12%, for CEYIELD, and 6.10%, for MASS. Therefore, the REML/Blup statistical tool was efficient in selecting top cross hybrids of green maize, providing significant genetic gains for the traits under evaluation. There was evidence that hybrids 19 and 48 were distinguished from others because of the high genetic effects obtained for the commercial ear yield and grain mass weight.
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Hoeschele, I., P. Uimari, F. E. Grignola, Q. Zhang, and K. M. Gage. "Advances in Statistical Methods to Map Quantitative Trait Loci in Outbred Populations." Genetics 147, no. 3 (November 1, 1997): 1445–57. http://dx.doi.org/10.1093/genetics/147.3.1445.
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Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLS on a chromosome as an unknown.
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Hashempour, Majid. "A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations." Mathematica Slovaca 71, no. 4 (August 1, 2021): 983–1004. http://dx.doi.org/10.1515/ms-2021-0034.
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Abstract In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.
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Boomsma, D. I., and P. C. M. Molenaar. "Constrained Maximum Likelihood Analysis of Familial Resemblance of Twins and Their Parents." Acta geneticae medicae et gemellologiae: twin research 36, no. 1 (January 1987): 29–39. http://dx.doi.org/10.1017/s0001566000004566.
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AbstractWhen the univariate twin design is extended by including parents of twins, it is possible to assess additive genetic effects in the presence of assortative mating and genotype-environment correlation, the effects of parental influence, as well as the extent of residual shared environmental influences. The analysis of data obtained in such an extended twin design can be carried out by means of constrained maximum likelihood confirmatory factor analysis. Specifically, the structural model underlying this design can be represented as a LISREL model with nonlinear constraints. This representation offers the possibility to consider extended multivariate twin designs involving common genetic and environmental factors. The proposed method will be illustrated with applications to simulated and real data.
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Bantan, Rashad, Amal S. Hassan, Mahmoud Elsehetry, and B. M. Golam Kibria. "Half-Logistic Xgamma Distribution: Properties and Estimation under Censored Samples." Discrete Dynamics in Nature and Society 2020 (June 17, 2020): 1–18. http://dx.doi.org/10.1155/2020/9136513.
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This paper proposed a new probability distribution, namely, the half-logistic xgamma (HLXG) distribution. Various statistical properties, such as, moments, incomplete moments, mean residual life, and stochastic ordering of the proposed distribution, are discussed. Parameter estimation of the half-logistic xgamma distribution is approached by the maximum likelihood method based on complete and censored samples. Asymptotic confidence intervals of model parameters are provided. A simulation study is conducted to illustrate the theoretical results. Moreover, the model parameters of the HLXG distribution are estimated by using the maximum likelihood, least square, maximum product spacing, percentile, and Cramer–von Mises (CVM) methods. Superiority of the new model over some existing distributions is illustrated through three real data sets.
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Liu, W. F., Y. F. Leung, and M. K. Lo. "Integrated framework for characterization of spatial variability of geological profiles." Canadian Geotechnical Journal 54, no. 1 (January 2017): 47–58. http://dx.doi.org/10.1139/cgj-2016-0189.
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Despite recent efforts to characterize the uncertainties involved with geological profiles and soil and rock properties, there has been limited study on their spatial correlations and how such features may be included in the engineering decision-making process. This paper presents an integrated framework for geostatisical analyses, which incorporates the restricted maximum likelihood (REML) method with the Matérn autocovariance model. Statistical tests are conducted including those for data normality, constant variance, and outliers, which ensure the fundamental assumptions of REML are not violated in the residual analyses of site data, meanwhile offering simple checks for potential errors in the dataset. The proposed approach also allows quantification of uncertainties in the subsurface profiles at the unsampled locations. The approach is illustrated through investigations on spatial correlation features of geological profiles at two project sites in Hong Kong. The number of irregularly spaced boreholes varies from 150 to 350 in the two cases, and the large volume of data enables the variations in rockhead levels to be studied through the proposed framework. In addition, the existence of geological faults in one of the sites is found to significantly affect the spatial variability of the rockhead level, as indicated by the reduced scales of fluctuation and spatial dependence, which corresponds to increased uncertainty in areas intersected by faults.
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Alves, Rodrigo, João Rocha, Larissa Teodoro, Luiz Carvalho, Francisco Farias, Marcos Resende, Leonardo Bhering, and Paulo Teodoro. "Path analysis under multiple-trait BLUP: application in the study of interrelationships among traits related to cotton fiber length." Revista de la Facultad de Ciencias Agrarias UNCuyo 53, no. 1 (July 7, 2021): 1–10. http://dx.doi.org/10.48162/rev.39.001.
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Multi-trait best linear unbiased prediction (BLUP) is, generally, the most appropriate method to genetic evaluation because it considers the genetic and residual correlations among traits and conduct to higher selection accuracy. Thus, the present study aimed to identify traits correlated to the fiber length via path analysis under multi-trait BLUP for the cotton breeding. To this end, thirty-six elite lines were evaluated in three environments and phenotyped for many traits related to fiber quality and agronomic traits. Variance components were estimated via residual maximum likelihood (REML). The genetic correlation coefficients among traits were obtained through mixed model output, and to graphically express these results a correlation network was built. Subsequently, we performed path analysis considering fiber length as a principal dependent variable. Genetic parameters obtained by multi-trait BLUP model indicate that the phenotypic variance for most traits is mostly composed of residual effects, which reinforces the need for using more accurate statistical methods such as multi-trait BLUP. The results found for genetic correlations and path analysis under multi-trait BLUP reveal the difficulty of selection based on important fiber quality traits, especially fiber length, since most traits show very low cause-and-effect relationship, and other important traits present undesirable cause-and-effect relationship.
Highlights
Multiple-trait BLUP is the most appropriate method to predict genetic values.
This is the first study in cotton to perform path analysis under multiple-trait BLUP.
The findings of this study indicate that there is no genotype presenting all desirable traits.
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Salahuddin, Najma, Alamgir Khalil, Wali Khan Mashwani, Habib Shah, Pijitra Jomsri, and Thammarat Panityakul. "A Novel Generalized Family of Distributions for Engineering and Life Sciences Data Applications." Mathematical Problems in Engineering 2021 (May 20, 2021): 1–16. http://dx.doi.org/10.1155/2021/9949999.
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In this paper, a new method is proposed to expand the family of lifetime distributions. The suggested method is named as Khalil new generalized family (KNGF) of distributions. A special submodel, termed as Khalil new generalized Pareto (KNGP) distribution, is investigated from the family with one shape and two scale parameters. A number of mathematical properties of the submodel have been derived including moments, moment-generating function, quantile function, entropy measures, order statistics, mean residual life function, and maximum likelihood method for the estimation of parameters. The proposed distribution is very flexible in its nature covering several hazard rate shapes (symmetric and asymmetric). To examine the performance of the maximum likelihood estimates in terms of their bias and mean squared error using simulated samples, a simulation study is carried out. Furthermore, parametric estimation of the model is conferred using the method of maximum likelihood, and the practicality of the proposed family is illustrated with the help of real datasets. Finally, we hope that the new suggested flexible KNGF may produce useful models for fitting monotonic and nonmonotonic data related to survival analysis and reliability analysis.
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El-Morshedy, M., and M. S. Eliwa. "The odd flexible Weibull-H family of distributions: Properties and estimation with applications to complete and upper record data." Filomat 33, no. 9 (2019): 2635–52. http://dx.doi.org/10.2298/fil1909635e.
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In this paper, a new generator of continuous distributions called the odd flexible Weibull-H family is proposed and studied. Some of its statistical properties including quantile, skewness, kurtosis, hazard rate function, moments, incomplete moments, mean deviations, coefficient of variation, Bonferroni and Lorenz curves, moments of the residual (past) lifetimes and entropies are studied. Two special models are introduced and discussed in-detail. The maximum likelihood method is used to estimate the model parameters based on complete and upper record data. Adetailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, three applications to real data sets show the flexibility of the new family.
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Mackie, J. M., P. M. Pepper, K. F. Lowe, J. M. Musial, and J. A. G. Irwin. "Potential to increase yield in lucerne (Medicago sativa subsp. sativa) through introgression of Medicago sativa subsp. falcata into Australian adapted material." Australian Journal of Agricultural Research 56, no. 12 (2005): 1365. http://dx.doi.org/10.1071/ar05085.
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The effect of interspecific heterosis in crosses between Medicago sativa subsp. sativa and M. sativa subsp. falcata was assessed. Three sativa and 3 falcata plants were crossed in a diallel design. Progeny dry matter yield and natural plant height were assessed in a replicated field experiment at Gatton, Queensland. Yield data were analysed using the method of residual maximum likelihood (REML) and Griffing’s model 1. There were significant differences between the reciprocal, general combining ability (GCA), and specific combining ability (SCA) effects. As expected, S1 populations were lower yielding than their respective intraspecific cross and falcata × falcata crosses were significantly lower yielding than sativa × sativa crosses. Some of the interspecific crosses indicated substantial SCA effects, yielding at least as well as the best sativa × sativa crosses. We have demonstrated the potential usefulness of unselected M. sativa subsp. falcata as a heterotic group in the improvement of yield in northern Australian adapted lucerne material, and discuss how it could be incorporated into future breeding to overcome the yield stagnation currently being experienced in Australian programs.
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VIRK, D. S., D. B. PANDIT, M. A. SUFIAN, F. AHMED, M. A. B. SIDDIQUE, M. A. SAMAD, M. M. RAHMAN, et al. "REML IS AN EFFECTIVE ANALYSIS FOR MIXED MODELLING OF UNBALANCED ON-FARM VARIETAL TRIALS." Experimental Agriculture 45, no. 1 (January 2009): 77–91. http://dx.doi.org/10.1017/s0014479708007047.
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SUMMARYOn-farm participatory varietal selection (PVS) trials are often of two types: mother trials (with all of the entries) and baby trials (each having one, or very few of the entries from the mother trials). We conducted PVS trials on 17 wheat varieties in 12 villages of four districts of Bangladesh over three years but the data were highly unbalanced. Both quantitative and qualitative traits were measured in the on-farm trials. The factors in the trials were both fixed effects (varieties and districts) and random (years and farmers). We used the residual or restricted maximum likelihood (REML) analysis for the mixed model for quantitative traits. For qualitative data on farmers' perceptions, logistic regression procedures were used that are equally applicable to balanced and unbalanced data sets. The REML analysis provided adjusted mean values for quantitative traits for all the varieties, for the mother and baby trials separately, using the data from all years and all locations. It identified varieties BAW 1006 and BAW 1008 that yielded 19–30% more than the control Kanchan and also had a higher 1000-grain weight, were at least as early to flower and had a high overall ranking by farmers in the mother trials. The logistic regression analysis of perception data agreed with the results of the REML analysis as these varieties were most preferred by farmers for grain yield, earlier maturity and better chapatti making quality. The less labour-intensive method of recording qualitative perceptions can usefully replace actual yield measurements, particularly when validated by other participatory measures such as intended and actual adoption. In 2005, BAW 1006 was released as BARI Gom 23 or Bijoy and BAW 1008 as BARI Gom 24 or Prodip for the whole of Bangladesh. The validity of the results of the REML analysis was confirmed by the high early adoption trends of the identified varieties. Since REML is an effective analysis for unbalanced PVS trial data using a mixed model, its wider use by researchers would increase the value of the PVS process.
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Bhatti, Fiaz Ahmad, G. G. Hamedani, Wenhui Sheng, and Munir Ahmad. "Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications." International Journal of Statistics and Probability 8, no. 1 (December 9, 2018): 94. http://dx.doi.org/10.5539/ijsp.v8n1p94.
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In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied.
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Bleed, Salma Omar, and Arwa Elsunousi Ali Abdelali. "TRANSMUTED ARCSINE DISTRIBUTION PROPERTIES AND APPLICATION." International Journal of Research -GRANTHAALAYAH 6, no. 10 (October 31, 2018): 38–47. http://dx.doi.org/10.29121/granthaalayah.v6.i10.2018.1159.
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The distribution of ArcSine will be developed to another new distribution using the Quadratic Rank Transmutation (QRT) method proposed by Shaw and Buckley (2007). The new distribution will be called the Transmuted ArcSine distribution, some of its mathematical characteristics such as variance, expectation, residual function, risk function, moments, moment generating function and characteristic function will be presented. The model parameters will be estimated by the maximum likelihood method. Finally, two real data sets are analyzed to illustrates the usefulness of the TAS distribution.
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Baskan, O., G. Erpul, and O. Dengiz. "Comparing the efficiency of ordinary kriging and cokriging to estimate the Atterberg limits spatially using some soil physical properties." Clay Minerals 44, no. 2 (June 2009): 181–93. http://dx.doi.org/10.1180/claymin.2009.044.2.181.
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AbstractThe spatial distribution of the Atterberg limits can be used to distinguish the consistency and behaviour of a soil and its engineering properties, which strongly depends on the water content of the soil and types of silts and clays in the soil. By spatial modeling, and comparing the results of ordinary kriging with the cokriging approach, this study aims to find correlations between the Atterberg limits and the selected physical soil parameters in order to examine how effective they are in generating an understanding of the dynamics of a physical soil system.In 156 soil samples, the Atterberg limits and soil moisture conditions were determined, and auxiliary functions were selected by application of cokriging using correlation analysis and regression equations obtained by the residual maximum likelihood (REML). These techniques were evaluated by the results of the mean absolute error (MAE) and the mean squared error (MSE). Cokriging analysis was found to be more effective at estimating the liquid limit (WLL) and the plastic limit (WPL) than kriging analysis and with smaller error values. On the other hand, the kriging approach, which had smaller MAE and MSE values, was more effective at estimating the plasticity index (WPI) values than the cokriging method. Unlike the REML regression equations, the field capacity (FC) value was the more suitable parameter for the cokriging estimates. When the necessary labour and time were considered for determining the Atterberg limits, both kriging and cokriging were found to be applicable for estimation of these limits.
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Muhammad, Mustapha, Huda M. Alshanbari, Ayed R. A. Alanzi, Lixia Liu, Waqas Sami, Christophe Chesneau, and Farrukh Jamal. "A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies." Entropy 23, no. 11 (October 24, 2021): 1394. http://dx.doi.org/10.3390/e23111394.
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In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.
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Korkmaz, Mustafa C., Emrah Altun, Haitham M. Yousof, and G. G. Hamedani. "The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling." International Journal of Statistics and Probability 8, no. 2 (January 25, 2019): 70. http://dx.doi.org/10.5539/ijsp.v8n2p70.
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In this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.
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Alotaibi, Naif, Ibrahim Elbatal, Ehab M. Almetwally, Salem A. Alyami, A. S. Al-Moisheer, and Mohammed Elgarhy. "Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data." Mathematics 10, no. 9 (May 6, 2022): 1565. http://dx.doi.org/10.3390/math10091565.
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The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions.
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Korkmaz, Mustafa Ç., Emrah Altun, Morad Alizadeh, and M. El-Morshedy. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model." Mathematics 9, no. 21 (October 20, 2021): 2634. http://dx.doi.org/10.3390/math9212634.
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Recently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.
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Mead, M. E., Ahmed Z. Afify, G. G. Hamedani, and Indranil Ghosh. "The Beta Exponential Fréchet Distribution with Applications." Austrian Journal of Statistics 46, no. 1 (January 4, 2017): 41–63. http://dx.doi.org/10.17713/ajs.v46i1.144.
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We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.
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Khalil, Alamgir, Abdullah Ali H. Ahmadini, Muhammad Ali, Wali Khan Mashwani, Shokrya S. Alshqaq, and Zabidin Salleh. "A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data." Journal of Mathematics 2021 (August 18, 2021): 1–13. http://dx.doi.org/10.1155/2021/4479270.
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In this paper, a new approach for deriving continuous probability distributions is developed by incorporating an extra parameter to the existing distributions. Frechet distribution is used as a submodel for an illustration to have a new continuous probability model, termed as modified Frechet (MF) distribution. Several important statistical properties such as moments, order statistics, quantile function, stress-strength parameter, mean residual life function, and mode have been derived for the proposed distribution. In order to estimate the parameters of MF distribution, the maximum likelihood estimation (MLE) method is used. To evaluate the performance of the proposed model, two real datasets are considered. Simulation studies have been carried out to investigate the performance of the parameters’ estimates. The results based on the real datasets and simulation studies provide evidence of better performance of the suggested distribution.
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Aidi, Khaoula, Amer Ibrahim Al-Omari, and Rehab Alsultan. "The Power Zeghdoudi Distribution: Properties, Estimation, and Applications to Real Right-Censored Data." Applied Sciences 12, no. 23 (November 25, 2022): 12081. http://dx.doi.org/10.3390/app122312081.
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A new two-parameter power Zeghdoudi distribution (PZD) is suggested as a modification of the Zeghdoudi distribution using the power transformation method. As a result, the PZD may have increasing, decreasing, and unimodal probability density function and decreasing mean residual life function. In addition, other properties are presented, such as moments, order statistics, reliability measures, Bonferroni and Lorenz curves, Gini index, stochastic ordering, mean and median deviations, and quantile function. Following this, a section is devoted to the related model parameters which are estimated using the maximum likelihood estimation method, the weighted least squares and least squares methods, the maximum product of spacing method, the Cramer–von Mises method, and the right-tail and left-tail Anderson–Darling methods, and the Nikulin–Rao–Robson test statistic is considered. A simulation study is conducted to assess these methods and to investigate the distribution properties with right-censored data. The applicability of the proposed model is studied based on three real data sets of failure times, bladder cancer patients, and glass fiber data with a comparison with such competitors as the gamma, xgamma, Lomax, Darna, power Darna, power Lindley, and exponentiated power Lindley models. According to several established criteria, the comparative findings are overwhelmingly favorable to the suggested model.
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Shanker, Rama, Kamlesh Kumar Shukla, and Hagos Fesshaye. "A GENERALIZATION OF SUJATHA DISTRIBUTION AND ITS APPLICATIONS WITH REAL LIFETIME DATA." Journal of Institute of Science and Technology 22, no. 1 (July 18, 2017): 66–83. http://dx.doi.org/10.3126/jist.v22i1.17742.
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A two-parameter generalization of Sujatha distribution (AGSD), which includes Lindley distribution and Sujatha distribution as particular cases, has been proposed. It's important mathematical and statistical properties including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Maximum likelihood estimation method has been discussed for estimating its parameters. AGSD provides better fit than Sujatha, Aradhana, Lindley and exponential distributions for modeling real lifetime data.Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 66-83
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Elbatal, Ibrahim, Naif Alotaibi, Ehab M. Almetwally, Salem A. Alyami, and Mohammed Elgarhy. "On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications." Symmetry 14, no. 5 (April 26, 2022): 883. http://dx.doi.org/10.3390/sym14050883.
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In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.
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Elbatal, Ibrahim, Naif Alotaibi, Ehab M. Almetwally, Salem A. Alyami, and Mohammed Elgarhy. "On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications." Symmetry 14, no. 5 (April 26, 2022): 883. http://dx.doi.org/10.3390/sym14050883.
Full textAbstract:
In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.
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Alyami, Salem, Moolath Girish Babu, Ibrahim Elbatal, Naif Alotaibi, and Mohammed Elgarhy. "Type II Half-Logistic Odd Fréchet Class of Distributions: Statistical Theory and Applications." Symmetry 14, no. 6 (June 13, 2022): 1222. http://dx.doi.org/10.3390/sym14061222.
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new class of statistical distributions called the Type II half-Logistic odd Fréchet-G class is proposed. The new class is a continuation of the unusual Fréchet class. This class is analytically feasible and could be used to evaluate real-world data effectively. The new suggested class of distributions has many new symmetrical and asymmetrical sub-models. We propose new four sub-models from the new class of distributions which are called Type II half-Logistic odd Fréchet exponential distribution, Type II half-Logistic odd Fréchet Rayleigh distribution, Type II half-Logistic odd FréchetWeibull distribution, and Type II half-Logistic odd Fréchet Lindley distribution. Some statistical features of Type II half-Logistic odd Fréchet-G class such as ordinary moments (ORMs), incomplete moments (INMs), moment generating function (MGEF), residual life (REL), and reversed residual life (RREL) functions, and Rényi entropy (RéE) are derived. Six methods of estimation such as maximum likelihood, least-square, a maximum product of spacing, weighted least square, Cram´ er-von Mises, and Anderson–Darling are produced to estimate the parameters. To test the six estimation methods’ performance, a simulation study is conducted. Four real-world data sets are utilized to highlight the importance and applicability of the proposed method.
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Alotaibi, Naif, and Igor V. Malyk. "A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications." Symmetry 12, no. 8 (August 10, 2020): 1338. http://dx.doi.org/10.3390/sym12081338.
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In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.
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Nisztuk, Sylwia, Brygida Ślaska, Grzegorz Zięba, and Iwona Rozempolska-Rucińska. "Association of MSTN gene polymorphism (C354T) with performance traits in raccoon dogs." Canadian Journal of Animal Science 98, no. 2 (June 1, 2018): 341–46. http://dx.doi.org/10.1139/cjas-2017-0070.
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The aim of the study was to identify polymorphisms within nuclear DNA genes and determine their association with the performance traits of farmed raccoon dogs. The study involved 354 animals and their breeding documentation data. Myostatin (MSTN), insulin-like growth factor 1 (IGF1), and growth hormone (GHR) genes were amplified, sequenced, and subjected to bioinformatics and statistical analysis. Estimation of variance components was performed with the residual maximum likelihood (REML) method, and best linear unbiased prediction (BLUP) of the breeding values was carried out. The predictors of the traits of direct additive, maternal additive, and random-specific maternal environmental effects were analysed. Within the nucleotide sequences of the analysed genes, one silent single nucleotide polymorphism (SNP) was identified in exon 1 of the MSTN gene. The analysis of the variance of the fixed-specific maternal environmental effect revealed statistically significant differences in the body weight among raccoon dogs with alternative polymorphisms. The mean effects of the estimators of polymorphism addition and dominance measured by MSTN gene regression had mostly a significant impact on the level of the traits estimated in animals. There was statistically significant association of the polymorphism in the MSTN gene with the body weight in raccoon dogs, which validates selection thereof as a candidate gene for this economically most important performance trait of raccoon dogs.
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Quintián, Héctor, and Emilio Corchado. "Beta Hebbian Learning as a New Method for Exploratory Projection Pursuit." International Journal of Neural Systems 27, no. 06 (March 16, 2017): 1750024. http://dx.doi.org/10.1142/s0129065717500241.
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In this research, a novel family of learning rules called Beta Hebbian Learning (BHL) is thoroughly investigated to extract information from high-dimensional datasets by projecting the data onto low-dimensional (typically two dimensional) subspaces, improving the existing exploratory methods by providing a clear representation of data’s internal structure. BHL applies a family of learning rules derived from the Probability Density Function (PDF) of the residual based on the beta distribution. This family of rules may be called Hebbian in that all use a simple multiplication of the output of the neural network with some function of the residuals after feedback. The derived learning rules can be linked to an adaptive form of Exploratory Projection Pursuit and with artificial distributions, the networks perform as the theory suggests they should: the use of different learning rules derived from different PDFs allows the identification of “interesting” dimensions (as far from the Gaussian distribution as possible) in high-dimensional datasets. This novel algorithm, BHL, has been tested over seven artificial datasets to study the behavior of BHL parameters, and was later applied successfully over four real datasets, comparing its results, in terms of performance, with other well-known Exploratory and projection models such as Maximum Likelihood Hebbian Learning (MLHL), Locally-Linear Embedding (LLE), Curvilinear Component Analysis (CCA), Isomap and Neural Principal Component Analysis (Neural PCA).
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Zou, Zhengting, Hongjiu Zhang, Yuanfang Guan, and Jianzhi Zhang. "Deep Residual Neural Networks Resolve Quartet Molecular Phylogenies." Molecular Biology and Evolution 37, no. 5 (December 23, 2019): 1495–507. http://dx.doi.org/10.1093/molbev/msz307.
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Abstract Phylogenetic inference is of fundamental importance to evolutionary as well as other fields of biology, and molecular sequences have emerged as the primary data for this task. Although many phylogenetic methods have been developed to explicitly take into account substitution models of sequence evolution, such methods could fail due to model misspecification or insufficiency, especially in the face of heterogeneities in substitution processes across sites and among lineages. In this study, we propose to infer topologies of four-taxon trees using deep residual neural networks, a machine learning approach needing no explicit modeling of the subject system and having a record of success in solving complex nonlinear inference problems. We train residual networks on simulated protein sequence data with extensive amino acid substitution heterogeneities. We show that the well-trained residual network predictors can outperform existing state-of-the-art inference methods such as the maximum likelihood method on diverse simulated test data, especially under extensive substitution heterogeneities. Reassuringly, residual network predictors generally agree with existing methods in the trees inferred from real phylogenetic data with known or widely believed topologies. Furthermore, when combined with the quartet puzzling algorithm, residual network predictors can be used to reconstruct trees with more than four taxa. We conclude that deep learning represents a powerful new approach to phylogenetic reconstruction, especially when sequences evolve via heterogeneous substitution processes. We present our best trained predictor in a freely available program named Phylogenetics by Deep Learning (PhyDL, https://gitlab.com/ztzou/phydl; last accessed January 3, 2020).
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Al-Babtain, Abdulhakim A., Abdul Hadi N. Ahmed, and Ahmed Z. Afify. "A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications." Entropy 22, no. 6 (May 28, 2020): 603. http://dx.doi.org/10.3390/e22060603.
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In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.
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Dey, Sanku, Enayetur Raheem, and Saikat Mukherjee. "Statistical properties and different methods of estimation of transmuted Rayleigh distribution." Revista Colombiana de Estadística 40, no. 1 (January 16, 2017): 165–203. http://dx.doi.org/10.15446/rce.v40n1.56153.
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This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median, the stochastic ordering, various entropies, stress-strength parameter and order statistics) are derived. We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings, method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.
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et al., Hassan. "A new generalization of the inverse Lomax distribution with statistical properties and applications." International Journal of ADVANCED AND APPLIED SCIENCES 8, no. 4 (April 2021): 89–97. http://dx.doi.org/10.21833/ijaas.2021.04.011.
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In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.
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Ferreira Coelho, Igor, Marco Antônio Peixoto, Jeniffer Santana Pinto Coelho Evangelista, Rodrigo Silva Alves, Suellen Sales, Marcos Deon Vilela de Resende, Jefferson Fernando Naves Pinto, Edésio Fialho dos Reis, and Leonardo Lopes Bhering. "Multiple-trait, random regression, and compound symmetry models for analyzing multi-environment trials in maize breeding." PLOS ONE 15, no. 11 (November 20, 2020): e0242705. http://dx.doi.org/10.1371/journal.pone.0242705.
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An efficient and informative statistical method to analyze genotype-by-environment interaction (GxE) is needed in maize breeding programs. Thus, the objective of this study was to compare the effectiveness of multiple-trait models (MTM), random regression models (RRM), and compound symmetry models (CSM) in the analysis of multi-environment trials (MET) in maize breeding. For this, a data set with 84 maize hybrids evaluated across four environments for the trait grain yield (GY) was used. Variance components were estimated by restricted maximum likelihood (REML), and genetic values were predicted by best linear unbiased prediction (BLUP). The best fit MTM, RRM, and CSM were identified by the Akaike information criterion (AIC), and the significance of the genetic effects were tested using the likelihood ratio test (LRT). Genetic gains were predicted considering four selection intensities (5, 10, 15, and 20 hybrids). The selected MTM, RRM, and CSM models fit heterogeneous residuals. Moreover, for RRM the genetic effects were modeled by Legendre polynomials of order two. Genetic variability between maize hybrids were assessed for GY. In general, estimates of broad-sense heritability, selective accuracy, and predicted selection gains were slightly higher when obtained using MTM and RRM. Thus, considering the criterion of parsimony and the possibility of predicting genetic values of hybrids for untested environments, RRM is a preferential approach for analyzing MET in maize breeding.
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Pang, Liyuan, Weizhong Tian, Tingting Tong, and Xiangfei Chen. "Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications." Modelling 2, no. 4 (December 15, 2021): 776–94. http://dx.doi.org/10.3390/modelling2040041.
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In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.
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Muhammad, Mustapha, Rashad A. R. Bantan, Lixia Liu, Christophe Chesneau, Muhammad H. Tahir, Farrukh Jamal, and Mohammed Elgarhy. "A New Extended Cosine—G Distributions for Lifetime Studies." Mathematics 9, no. 21 (October 30, 2021): 2758. http://dx.doi.org/10.3390/math9212758.
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In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.
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El-Morshedy, Mahmoud, Morad Alizadeh, Afrah Al-Bossly, and Mohamed Eliwa. "A Probability Mass Function for Various Shapes of the Failure Rates, Asymmetric and Dispersed Data with Applications to Coronavirus and Kidney Dysmorphogenesis." Symmetry 13, no. 10 (September 26, 2021): 1790. http://dx.doi.org/10.3390/sym13101790.
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In this article, a discrete analogue of an extension to a two-parameter half-logistic model is proposed for modeling count data. The probability mass function of the new model can be expressed as a mixture representation of a geometric model. Some of its statistical properties, including hazard rate function, moments, moment generating function, conditional moments, stress-strength analysis, residual entropy, cumulative residual entropy and order statistics with its moments, are derived. It is found that the new distribution can be utilized to model positive skewed data, and it can be used for analyzing equi- and over-dispersed data. Furthermore, the hazard rate function can be either decreasing, increasing or bathtub. The parameter estimation through the classical point of view has been performed using the method of maximum likelihood. A detailed simulation study is carried out to examine the outcomes of the estimators. Finally, two distinctive real data sets are analyzed to prove the flexibility of the proposed discrete distribution.
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Aguilar, Guilherme Aparecido Santos, Fernando A. Moala, and Ricardo Puziol de Oliveira. "Marshall olkin extended exponentiated Gamma distribution and its applications." Model Assisted Statistics and Applications 17, no. 2 (May 23, 2022): 123–41. http://dx.doi.org/10.3233/mas-220015.
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Different methods for obtaining new probability distributions have been introduced in the literature in recent years, for example, (Gupta et al., 1998) proposed an interesting uni-parametric lifetime distribution, Exponentiated Gamma (EG), which hazard function has increasing and bathtub shapes. In this paper, we build a new two-parameters distribution, the Marshall Olkin Extended Exponentiated Gamma (MOEEG) distribution, which is derived from the Marshall-Olkin method and the EG distribution. The hazard function of this new distribution can accommodate monotonic, non-monotonic and unimodal shapes, allowing a better fit to greater data variability. In addition to the great flexibility of fitting the data, it contains only two parameters providing a simple parameter estimation procedure, unlike other distributions proposed in the literature that have three or more parameters. Some properties of the new distribution considered in this paper are presented such as n-th time, r-th moment of residual life, r-thmoment of residual life inverted, stochastic ordering, entropy, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics, and stress-strength parameter. We also apply two different estimation methods, maximum likelihood and Bayesian approach. Real data applications are presented to illustrate the usefulness of this new distribution.
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Badmus, Nofiu Idowu, Mary Idowu Akinyemi, and Josephine Nneamaka Onyeka-Ubaka. "A Log-Beta Rayleigh Lomax Regression Model." Afrika Statistika 16, no. 4 (October 1, 2021): 2993–3007. http://dx.doi.org/10.16929/as/2021.2993.192.
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For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.
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Bararyenya, Astere, Phinehas Tukamuhabwa, Paul Gibson, Wolfgang Gruneberg, Reuben Ssali, Jan Low, Thomas Odong, et al. "Continuous Storage Root Formation and Bulking in Sweetpotato." Gates Open Research 3 (February 11, 2019): 83. http://dx.doi.org/10.12688/gatesopenres.12895.1.
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This study investigated the phenotypic variation of continuous storage root formation and bulking (CSRFAB) growth patterns underlying the development of sweetpotato genotypes for identification of potential varieties adapted to piecemeal harvesting for small scale farmers. The research was conducted between September 2016 and August 2017 in Uganda. Genotypes from two distinct sweetpotato genepool populations (Population Uganda A and Population Uganda B) comprising 130 genotypes, previously separated using 18 simple sequence repeat (SSR) markers were used. Repeated measurements (4 harvest times with 4 plants each) on genotypes in a randomized complete block design with 2 replications in 2 locations for 2 seasons were used. We developed a scoring scale of 1 to 9 and used it to compare growth changes between consecutive harvests. Data analysis was done using residual or restricted maximum likelihood (REML) in GenStat 18th Edition. There were strong linear and quadratic trends over time (P<0.001) indicating a non-linear growth pattern within and between locations, seasons, and genotypes for most traits. Some genotypes displayed early initiation and a determinate linear increase of bulking, while others showed late initiation following a quadratic growth pattern. Broad sense heritability of CSRFAB would be low due to large GxE interactions, however, it was relatively high (50.5%) compared to other yield related traits indicating high genetic influence and accuracy of the developed method to quantify yield overtime. High level of reproducibility (89%) was observed comparing 2017A and 2017B seasons at Namulonge (NaCRRI). Choosing CSRFAB genotype can more than double the sweetpotato production (average maximum yield of 13.1 t/ha for discontinuous storage root formation and bulking (DSRFAB) versus 28.6 t/ha for CSRFAB demonstrating the importance of this under researched component of storage root yield.
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Bararyenya, Astere, Phinehas Tukamuhabwa, Paul Gibson, Wolfgang Grüneberg, Reuben Ssali, Jan Low, Thomas Odong, et al. "Continuous Storage Root Formation and Bulking in Sweetpotato." Gates Open Research 3 (October 14, 2019): 83. http://dx.doi.org/10.12688/gatesopenres.12895.2.
Full textAbstract:
This study investigated the phenotypic variation of continuous storage root formation and bulking (CSRFAB) growth patterns underlying the development of sweetpotato genotypes for identification of potential varieties adapted to piecemeal harvesting for small scale farmers. The research was conducted between September 2016 and August 2017 in Uganda. Genotypes from two distinct sweetpotato genepool populations (Population Uganda A and Population Uganda B) comprising 130 genotypes, previously separated using 31 simple sequence repeat (SSR) markers were used. Measurements (4 harvest times with 4 plants each) were repeated on genotypes in a randomized complete block design with 2 replications in 2 locations for 2 seasons. We developed a scoring scale of 1 to 9 and used it to compare growth changes between consecutive harvests. Data analysis was done using residual or restricted maximum likelihood (REML) in GenStat 18th Edition. There were strong linear and quadratic trends over time (P<0.001) indicating a non-linear growth pattern within and between locations, seasons, and genotypes for most traits. Some genotypes displayed early initiation and a determinate linear increase of bulking, while others showed late initiation following a quadratic growth pattern. Broad sense heritability of CSRFAB would be low due to large GxE interactions, however, it was relatively high (50.5%) compared to other yield related traits indicating high genetic influence and accuracy of the developed method to quantify yield overtime. A high level of reproducibility (89%) was observed comparing 2017A and 2017B seasons (A and B are first and second season, respectively) at the National Crops Resources Research Institute (NaCRRI), Namulonge, Uganda. Choosing CSRFAB genotypes can more than double the sweetpotato production (average maximum yield of 13.1 t/ha for discontinuous storage root formation and bulking (DSRFAB) versus 28.6 t/ha for CSRFAB demonstrating the importance of this underresearched component of storage root yield.
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Bararyenya, Astere, Phinehas Tukamuhabwa, Paul Gibson, Wolfgang Grüneberg, Reuben Ssali, Jan Low, Thomas Odong, et al. "Continuous Storage Root Formation and Bulking in Sweetpotato." Gates Open Research 3 (April 8, 2020): 83. http://dx.doi.org/10.12688/gatesopenres.12895.3.
Full textAbstract:
This study investigated the phenotypic variation of continuous storage root formation and bulking (CSRFAB) growth patterns underlying the development of sweetpotato genotypes for identification of potential varieties adapted to piecemeal harvesting for small scale farmers. The research was conducted between September 2016 and August 2017 in Uganda. Genotypes from two distinct sweetpotato genepool populations (Population Uganda A and Population Uganda B) comprising 130 genotypes, previously separated using 31 simple sequence repeat (SSR) markers were used. Measurements (4 harvest times with 4 plants each) were repeated on genotypes in a randomized complete block design with 2 replications in 2 locations for 2 seasons. We developed a scoring scale of 1 to 9 and used it to compare growth changes between consecutive harvests. Data analysis was done using residual or restricted maximum likelihood (REML) in GenStat 18th Edition. There were strong linear and quadratic trends over time (P<0.001) indicating a non-linear growth pattern within and between locations, seasons, and genotypes for most traits. Some genotypes displayed early initiation and a determinate linear increase of bulking, while others showed late initiation following a quadratic growth pattern. Broad sense heritability of CSRFAB would be low due to large GxE interactions, however, it was relatively high (50.5%) compared to other yield related traits indicating high genetic influence and accuracy of the developed method to quantify yield overtime. A high level of reproducibility (89%) was observed comparing 2016B and 2017A seasons (A and B are first and second season, respectively) at the National Crops Resources Research Institute (NaCRRI), Namulonge, Uganda. Choosing CSRFAB genotypes can more than double the sweetpotato production (average maximum yield of 13.1 t/ha for discontinuous storage root formation and bulking (DSRFAB) versus 28.6 t/ha for CSRFAB demonstrating the importance of this underresearched component of storage root yield.
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LOUZADA, Francisco, Ibrahim ELBATAL, and Daniele Cristina Tita GRANZOTTO. "THE TRANSMUTED GENERALIZED LINDLEY DISTRIBUTION: PROPERTIES AND AN APPLICATION TO A DATA SET ON TIME-UP-TO-CURE OF PATIENTS TREATED WITH A TRIAZOLE ANTIFUNGAL DRUG IN AN INTENSIVE CARE UNIT." REVISTA BRASILEIRA DE BIOMETRIA 36, no. 2 (June 28, 2018): 385. http://dx.doi.org/10.28951/rbb.v36i2.207.
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In this paper, we consider transmuted generalized Lindley distribution, obtained via the quadratic rank transmutation map under the Lindley distribution. This distribution exhibits, in addition to decreasing, increasing and bathtub hazard rates, depending on its parameters, also unimodal hazard rate shape. A comprehensive mathematical treatment of this distribution is provided. Expressions for the moment generating function, moments, order statistics, residual life and reversed failure rate function are derived. The model parameters are estimated by the maximum likelihood method. A simulation study is performed to verify the behavior of the estimation procedure in terms of mean square errors and coverage probability. Global and local influence diagnostic procedures are provided. We then analyse a real data set on time-up-to-cure of patients treated with a triazole antifungal drug in an intensive care unit in Brazil.
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Mohammadi, Ali, Sadegh Alijani, and Hossein Daghighkia. "Comparison of different polynomial functions in Random Regression Model for milk production traits of Iranian Holstein dairy cattle." Annals of Animal Science 14, no. 1 (March 1, 2014): 55–68. http://dx.doi.org/10.2478/aoas-2013-0078.
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Abstract The aim of this research was to compare different polynomial functions including Legendre polynomials (LP), Wilmink (WRR) and Ali-Schaeffer (ARR) functions, in random regression model (RRM) for estimation of genetic parameters for milk production traits of Iranian Holstein dairy cattle. For this purpose the performance records obtained from test-day (TD) regarding milk yield, fat and protein contents of the cows calving for the first time were used. The numbers of records for the above mentioned traits were 701212, 657004, and 560775, respectively. These records were collected from the years 2006 to 2010 by the National Breeding Center of Iran. The genetic parameters were estimated using Restricted Maximum Likelihood (REML) method by applying RRM. Residual variances were considered homogeneous over the lactation period. To compare the model, different criteria (-2Logl, AIC, BIC and RV) were used for considered traits. Based on the results obtained, for all traits, RRM with LP function (2,5) were chosen as the best model. Considering residual variance (RV), LP (2,2) was proved to be a model which has the lowest performance, while using -2Logl, AIC, BIC criteria, RRM with ARR function was the worst model. According to the results, it is recommended to use LP with low orders for the additive genetic effects and with more orders for the permanent environment effects in the RRM for Iranian Holstein cattle. Permanent environment variance was higher in early lactation than during lactation and additive genetic variance in the early lactation was lower than at the end of lactation. Heritability range of milk yield, fat and protein contents was estimated to be from 0.08 to 0.23, 0.05 to 0.20 and 0.08 to 0.14, respectively. Phenotypic variance of the considered traits during lactation was not constant and it was higher at the beginning and the end of lactation. The additive genetic correlation between adjacent test days was higher than between distant test days.
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Ghosh, Indranil, Sanku Dey, and Devendra Kumar. "Bounded M-O Extended Exponential Distribution with Applications." Stochastics and Quality Control 34, no. 1 (June 1, 2019): 35–51. http://dx.doi.org/10.1515/eqc-2018-0028.
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Abstract In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95 asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.
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Ramos, Pedro L., and Francisco Louzada. "A Distribution for Instantaneous Failures." Stats 2, no. 2 (May 7, 2019): 247–58. http://dx.doi.org/10.3390/stats2020019.
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A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.
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Ali, Muhammad, Alamgir Khalil, Muhammad Ijaz, and Noor Saeed. "Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data." PLOS ONE 16, no. 1 (January 14, 2021): e0245253. http://dx.doi.org/10.1371/journal.pone.0245253.
Full textAbstract:
The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.