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Journal articles on the topic 'Flexible distributions'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Arnold, Barry C., and Hon Keung Tony Ng. "Flexible bivariate beta distributions." Journal of Multivariate Analysis 102, no. 8 (September 2011): 1194–202. http://dx.doi.org/10.1016/j.jmva.2011.04.001.

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2

Quintana, Fernando A., Mark F. J. Steel, and José T. A. S. Ferreira. "Flexible univariate continuous distributions." Bayesian Analysis 4, no. 3 (September 2009): 497–521. http://dx.doi.org/10.1214/09-ba418.

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3

Fosgerau, Mogens, and Stefan L. Mabit. "Easy and flexible mixture distributions." Economics Letters 120, no. 2 (August 2013): 206–10. http://dx.doi.org/10.1016/j.econlet.2013.03.050.

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4

Ch, V. Sastry. "Marshall-Olkin Stereographic Circular Logistic Distribution." YMER Digital 21, no. 06 (June 22, 2022): 664–68. http://dx.doi.org/10.37896/ymer21.06/66.

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Marshall and Olkin (1997) proposed an interesting method of adding a new parameter to the existing distributions. The resulting distributions are called the MarshallOlkin distributions, these distributions include the original distributions as a special case and are more flexible and represent a wide range of behavior than the original distributions. In this paper, a new class of asymmetric stereographic circular logistic distribution is introduced by using Marshall-Olkin transformation on stereographic circular logistic distribution (Dattatreyarao et al (2016)), named as Marshall-Olkin Stereographic Circular Logistic Distribution. The proposed model admits closed form density and distribution functions, generalizes the stereographic circular logistic model and is more flexible to model various types of data (symmetric and skew-symmetric circular data). Keywords:Characteristics, Stereographic circular logistic distribution, circular data, Marshall-Olkin transformation, l -axial data.

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5

Hansen, Christian, James B. McDonald, and Whitney K. Newey. "Instrumental Variables Estimation With Flexible Distributions." Journal of Business & Economic Statistics 28, no. 1 (January 2010): 13–25. http://dx.doi.org/10.1198/jbes.2009.06161.

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Ma, Yanyuan, and Marc G. Genton. "Flexible Class of Skew-Symmetric Distributions." Scandinavian Journal of Statistics 31, no. 3 (September 2004): 459–68. http://dx.doi.org/10.1111/j.1467-9469.2004.03_007.x.

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Tovissodé, Chénangnon Frédéric, Sèwanou Hermann Honfo, Jonas Têlé Doumatè, and Romain Glèlè Kakaï. "On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism." Mathematics 9, no. 5 (March 6, 2021): 555. http://dx.doi.org/10.3390/math9050555.

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Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

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SHANG, JEN S., and PANDU R. TADIKAMALLA. "MODELING FINANCIAL SERIES DISTRIBUTIONS: A VERSATILE DATA FITTING APPROACH." International Journal of Theoretical and Applied Finance 07, no. 03 (May 2004): 231–51. http://dx.doi.org/10.1142/s0219024904002475.

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The empirical distribution of common stock returns is a subject of interest to many researchers, as it often determines the validity of theoretical models proposed in the economics and finance studies. This paper brings to the attention the availability of two flexible systems of distributions for fitting data: the Johnson system of distributions and the Tadikamalla–Johnson system of distributions. We explore the feasibility of fitting the empirical distributions of several financial series to these two systems of distributions. Both systems of distributions are highly flexible and capable of accommodating all possible skewness and kurtosis values. The probability density function and the cumulative distribution function take on simple closed forms and appropriate transformations of the data lead to normal/logistic distributions. In addition, the parameter estimation procedures are easy to implement. When the results are compared with those of other data fitting models, in all cases tested, the proposed distributions provide a good fit to the empirical distribution of data.

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Alkhairy, Ibrahim, Humaira Faqiri, Zubir Shah, Hassan Alsuhabi, M. Yusuf, Ramy Aldallal, Nicholas Makumi, and Fathy H. Riad. "A New Flexible Logarithmic-X Family of Distributions with Applications to Biological Systems." Complexity 2022 (August 30, 2022): 1–15. http://dx.doi.org/10.1155/2022/7845765.

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Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic- X (NFLog- X ) family. The suggested NFLog- X family is obtained by applying the T- X method together with the exponential model having the PDF m t = e − t . Based on the NFLog- X approach, a three parameters probability distribution, namely, a new flexible logarithmic-Weibull (NFLog-Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog- X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog-Wei distribution. Comparisons are made between the analytical goodness-of-fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic-Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

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10

Smith, Valerie A., and John S. Preisser. "Direct and flexible marginal inference for semicontinuous data." Statistical Methods in Medical Research 26, no. 6 (September 1, 2015): 2962–65. http://dx.doi.org/10.1177/0962280215602290.

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The marginalized two-part (MTP) model for semicontinuous data proposed by Smith et al. provides direct inference for the effect of covariates on the marginal mean of positively continuous data with zeros. This brief note addresses mischaracterizations of the MTP model by Gebregziabher et al. Additionally, the MTP model is extended to incorporate the three-parameter generalized gamma distribution, which takes many well-known distributions as special cases, including the Weibull, gamma, inverse gamma, and log-normal distributions.

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11

Ahmad, Zubair, and Brikhna Iqbal. "Generalized Flexible Weibull Extension Distribution." Circulation in Computer Science 2, no. 4 (May 20, 2017): 68–75. http://dx.doi.org/10.22632/ccs-2017-252-11.

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In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

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12

Brockett, Patrick L., Linda L. Golden, and Harry H. Panjer. "Flexible Purchase Frequency Modeling." Journal of Marketing Research 33, no. 1 (February 1996): 94–107. http://dx.doi.org/10.1177/002224379603300109.

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The authors present a general framework for purchase frequency modeling that enables flexible fitting and convenient computation. Their easily described purchase frequency distributions subsume many previous models and provide a connection between mixed Poisson marketing models and the conceptually distinct compound Poisson models. These distributions provide simple parametric equations for individual-level prediction of second-period purchase frequency based on observed first-period purchase frequencies. The results are applied to four marketing panel data sets.

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Tashpulatov, Sherzod N. "Modeling Electricity Price Dynamics Using Flexible Distributions." Mathematics 10, no. 10 (May 21, 2022): 1757. http://dx.doi.org/10.3390/math10101757.

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We consider the wholesale electricity market prices in England and Wales during its complete history, where price-cap regulation and divestment series were introduced at different points in time. We compare the impact of these regulatory reforms on the dynamics of electricity prices. For this purpose, we apply flexible distributions that account for asymmetry, heavy tails, and excess kurtosis usually observed in data or model residuals. The application of skew generalized error distribution is appropriate for our case study. We find that after the second series of divestments, price level and volatility are lower than during price-cap regulation and after the first series of divestments. This finding implies that a sufficient horizontal restructuring through divestment series may be superior to price-cap regulation. The conclusion could be interesting to other countries because the England and Wales electricity market served as the benchmark model for liberalizing energy markets worldwide.

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Park, Sangun, and Jiwhan Park. "A general class of flexible Weibull distributions." Communications in Statistics - Theory and Methods 47, no. 4 (December 26, 2017): 767–78. http://dx.doi.org/10.1080/03610926.2015.1118509.

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15

Arnold, Barry C. "A flexible family of multivariate Pareto distributions." Journal of Statistical Planning and Inference 24, no. 2 (February 1990): 249–58. http://dx.doi.org/10.1016/0378-3758(90)90045-v.

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Sommerfeldt, Scott D., and Lance B. Bischoff. "Vibration distributions of adaptively controlled flexible plates." Journal of the Acoustical Society of America 88, S1 (November 1990): S101. http://dx.doi.org/10.1121/1.2028468.

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17

Zhang, Yuanyuan, and Saralees Nadarajah. "Flexible Heavy Tailed Distributions for Big Data." Annals of Data Science 4, no. 3 (June 10, 2017): 421–32. http://dx.doi.org/10.1007/s40745-017-0113-4.

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18

Lee, Katherine J., and Simon G. Thompson. "Flexible parametric models for random-effects distributions." Statistics in Medicine 27, no. 3 (2008): 418–34. http://dx.doi.org/10.1002/sim.2897.

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Shi, Xue, Yu Li, and Quanhua Zhao. "Flexible Hierarchical Gaussian Mixture Model for High-Resolution Remote Sensing Image Segmentation." Remote Sensing 12, no. 7 (April 9, 2020): 1219. http://dx.doi.org/10.3390/rs12071219.

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The Gaussian mixture model (GMM) plays an important role in image segmentation, but the difficulty of GMM for modeling asymmetric, heavy-tailed, or multimodal distributions of pixel intensities significantly limits its application. One effective way to improve the segmentation accuracy is to accurately model the statistical distributions of pixel intensities. In this study, an innovative high-resolution remote sensing image segmentation algorithm is proposed based on a flexible hierarchical GMM (HGMM). The components are first defined by the weighted sums of elements, in order to accurately model the complicated distributions of pixel intensities in object regions. The elements of components are defined by Gaussian distributions to model the distributions of pixel intensities in local regions of the object region. Following the Bayesian theorem, the segmentation model is then built by combining the HGMM and the prior distributions of parameters. Finally, a novel birth or death Markov chain Monte Carlo (BDMCMC) is designed to simulate the segmentation model, which can automatically determine the number of elements and flexibly model complex distributions of pixel intensities. Experiments were implemented on simulated and real high-resolution remote sensing images. The results show that the proposed algorithm is able to flexibly model the complicated distributions and accurately segment images.

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20

Jana, Sumitash, Atul Gopal, and Aditya Murthy. "Evidence of common and separate eye and hand accumulators underlying flexible eye-hand coordination." Journal of Neurophysiology 117, no. 1 (January 1, 2017): 348–64. http://dx.doi.org/10.1152/jn.00688.2016.

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Eye and hand movements are initiated by anatomically separate regions in the brain, and yet these movements can be flexibly coupled and decoupled, depending on the need. The computational architecture that enables this flexible coupling of independent effectors is not understood. Here, we studied the computational architecture that enables flexible eye-hand coordination using a drift diffusion framework, which predicts that the variability of the reaction time (RT) distribution scales with its mean. We show that a common stochastic accumulator to threshold, followed by a noisy effector-dependent delay, explains eye-hand RT distributions and their correlation in a visual search task that required decision-making, while an interactive eye and hand accumulator model did not. In contrast, in an eye-hand dual task, an interactive model better predicted the observed correlations and RT distributions than a common accumulator model. Notably, these two models could only be distinguished on the basis of the variability and not the means of the predicted RT distributions. Additionally, signatures of separate initiation signals were also observed in a small fraction of trials in the visual search task, implying that these distinct computational architectures were not a manifestation of the task design per se. Taken together, our results suggest two unique computational architectures for eye-hand coordination, with task context biasing the brain toward instantiating one of the two architectures.NEW & NOTEWORTHY Previous studies on eye-hand coordination have considered mainly the means of eye and hand reaction time (RT) distributions. Here, we leverage the approximately linear relationship between the mean and standard deviation of RT distributions, as predicted by the drift-diffusion model, to propose the existence of two distinct computational architectures underlying coordinated eye-hand movements. These architectures, for the first time, provide a computational basis for the flexible coupling between eye and hand movements.

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Zhou, M., D. Yang, Y. Wang, and S. Nadarajah. "CONDITIONAL POISSON DISTRIBUTIONS." Probability in the Engineering and Informational Sciences 20, no. 1 (December 12, 2005): 95–102. http://dx.doi.org/10.1017/s0269964806060050.

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Compared to the known univariate distributions for continuous data, there are relatively few available for discrete data. In this article, we derive a collection of 16 flexible discrete distributions by means of conditional Poisson processes. The calculations involve the use of several special functions and their properties.

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22

Liu, Yinglin, Muhammad Ilyas, Saima K. Khosa, Eisa Muhmoudi, Zubair Ahmad, Dost Muhammad Khan, and G. G. Hamedani. "A Flexible Reduced Logarithmic-X Family of Distributions with Biomedical Analysis." Computational and Mathematical Methods in Medicine 2020 (February 20, 2020): 1–15. http://dx.doi.org/10.1155/2020/4373595.

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Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such data sets. In the present study, therefore, we propose a new family of distributions to model right skewed medical data sets. The proposed family may be named as a flexible reduced logarithmic-X family. The proposed family can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. A special submodel of the proposed family called, a flexible reduced logarithmic-Weibull distribution, is discussed in detail. Some mathematical properties of the proposed family and certain related characterization results are presented. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is done to evaluate the performance of these estimators. Finally, for the illustrative purposes, three applications from biomedical sciences are analyzed and the goodness of fit of the proposed distribution is compared to some well-known competitors.

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Al-Marzouki, Sanaa, and Sharifah Alrajhi. "A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution." Journal of Computational and Theoretical Nanoscience 17, no. 11 (November 1, 2020): 4813–18. http://dx.doi.org/10.1166/jctn.2020.9332.

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We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

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LIUTI, SIMONETTA, GARY R. GOLDSTEIN, J. OSVALDO GONZALEZ HERNANDEZ, and KUNAL KATHURIA. "RELATIONS BETWEEN TRANSVERSE MOMENTUM DISTRIBUTIONS AND CHIRAL ODD GENERALIZED PARTON DISTRIBUTIONS." International Journal of Modern Physics: Conference Series 20 (January 2012): 230–37. http://dx.doi.org/10.1142/s2010194512009282.

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We discuss the information on the spin structure of the proton that one can access by studying transverse momentum distributions, generalized parton distributions and their connection through generalized transverse momentum distributions. A "flexible" parametrization is proposed to extract this information from deeply virtual exclusive experiments.

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Alhaji Modu Isa, Sule Omeiza Bashiru, Alhaji Buhari Ali, Akeem Ajibola Adepoju, and Ibrahim Ismaila Itopa. "Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset." UMYU Scientifica 1, no. 1 (September 30, 2022): 127–31. http://dx.doi.org/10.56919/usci.1122.017.

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To increase flexibility or to develop covariate models in various ways, new parameters can be added to existing families of distributions or a new family of distributions can be compounded with well-known standard normal distribution. In this paper, a trigonometric-type distribution was developed in order to come up with flexible distribution without adding parameters, considering Exponential distribution as the baseline distribution and Sine-G as the generator. The proposed distribution is referred to as Sine Exponential Distribution. Statistical features, including the moment, moment generating function, entropy, and order statistics were obtained. The proposed distribution's parameters were estimated using the Maximum Likelihood method. Using real datasets, the model's importance was demonstrated. The newly developed model was proven to be better than its competitors.

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Timm, David H., and Eugene L. Skok. "Impact of Assumed Versus Measured Vehicle Distributions on County Road Flexible Pavement Design." Transportation Research Record: Journal of the Transportation Research Board 1819, no. 1 (January 2003): 244–50. http://dx.doi.org/10.3141/1819b-31.

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Accurate characterization of traffic is critical to the design of pavement structures. At the low-volume road level, a common practice is to use assumed vehicle type distributions based on statewide or regional studies instead of measuring the traffic for a particular location. The impact of this practice was investigated, and equivalent single-axle loads determined from measured vehicle distributions on 29 county roads in Minnesota were compared with those calculated from assumed distributions. It was found that significant differences exist between the assumed distribution and the measured distribution. Additionally, the impact of using assumed distributions on the structural design of flexible pavements was investigated. With data collected from 21 different county roads in Minnesota, it was found that using assumed distributions can result in over- or under-designed pavements, with asphalt concrete thicknesses often deviating by more than 50 mm (2 in.). Based on the results, it was recommended that Minnesota counties begin to evaluate when more detailed traffic studies are warranted to improve their designs and use of resources.

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27

Branscum, Adam J., Wesley O. Johnson, and Andre T. Baron. "Robust Medical Test Evaluation Using Flexible Bayesian Semiparametric Regression Models." Epidemiology Research International 2013 (December 11, 2013): 1–8. http://dx.doi.org/10.1155/2013/131232.

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The application of Bayesian methods is increasing in modern epidemiology. Although parametric Bayesian analysis has penetrated the population health sciences, flexible nonparametric Bayesian methods have received less attention. A goal in nonparametric Bayesian analysis is to estimate unknown functions (e.g., density or distribution functions) rather than scalar parameters (e.g., means or proportions). For instance, ROC curves are obtained from the distribution functions corresponding to continuous biomarker data taken from healthy and diseased populations. Standard parametric approaches to Bayesian analysis involve distributions with a small number of parameters, where the prior specification is relatively straight forward. In the nonparametric Bayesian case, the prior is placed on an infinite dimensional space of all distributions, which requires special methods. A popular approach to nonparametric Bayesian analysis that involves Polya tree prior distributions is described. We provide example code to illustrate how models that contain Polya tree priors can be fit using SAS software. The methods are used to evaluate the covariate-specific accuracy of the biomarker, soluble epidermal growth factor receptor, for discerning lung cancer cases from controls using a flexible ROC regression modeling framework. The application highlights the usefulness of flexible models over a standard parametric method for estimating ROC curves.

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Farooq, Muhammad, Qamruz zaman, Muhammad Ijaz, Said Farooq Shah, and Mutua Kilai. "A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets." Mathematical Problems in Engineering 2021 (July 30, 2021): 1–11. http://dx.doi.org/10.1155/2021/9717872.

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In practice, the data sets with extreme values are possible in many fields such as engineering, lifetime analysis, business, and economics. A lot of probability distributions are derived and presented to increase the model flexibility in the presence of such values. The current study also focuses on investigations to derive a new probability model New Flexible Family (NFF) of distributions. The significance of NFF is carried out using the Weibull distribution called New Flexible Weibull distribution or in short NFW. Various mathematical properties of NFW have been discussed including the estimation of parameters and entropy measures. Two real data sets with extreme values and a simulation study have been conducted so as to delineate the importance of NFW. Furthermore, NFW is compared with other existing probability distributions; numerically, it has been observed that the new mechanism of producing the lifetime probability distributions plays a significant role in making predictions about the population than others using the data sets with extreme values.

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Reyes, Jimmy, Mario A. Rojas, Pedro L. Cortés, and Jaime Arrué. "A New More Flexible Class of Distributions on (0,1): Properties and Applications to Univariate Data and Quantile Regression." Symmetry 15, no. 2 (January 18, 2023): 267. http://dx.doi.org/10.3390/sym15020267.

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In this paper, we will present a new, more flexible class of distributions with a domain in the interval (0,1), which presents heavier tails than other distributions in the same domain, such as the Beta, Kumaraswamy, and Weibull Unitary distributions. This new distribution is obtained as a transformation of two independent random variables with a Weibull distribution, which we will call the Generalized Unitary Weibull distribution. Considering a particular case, we will obtain an alternative to the Beta, Kumaraswamy, and Weibull Unitary distributions. We will call this new distribution of two parameters the type 2 unitary Weibull distribution. The probability density function, cumulative probability distribution, survival function, hazard rate, and some important properties that will allow us to infer are provided. We will carry out a simulation study using the maximum likelihood method and we will analyze the behavior of the parameter estimates. By way of illustration, real data will be used to show the flexibility of the new distribution by comparing it with other distributions that are known in the literature. Finally, we will show a quantile regression application, where it is shown how the proposed distribution fits better than other competing distributions for this type of application.

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Tanprayoon, Ekapak, Unchalee Tonggumnead, and Sirinapa Aryuyuen. "A New Extension of Generalized Extreme Value Distribution: Extreme Value Analysis and Return Level Estimation of the Rainfall Data." Trends in Sciences 20, no. 1 (November 26, 2022): 4034. http://dx.doi.org/10.48048/tis.2023.4034.

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This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go-GEV was an alternative flexible distribution for extreme values that fitted with actual data and described the maximum rainfall better than the traditional GEV distribution. The probability density functions of the Go-GEV distribution had various shapes including left-skewed, right-skewed and close to symmetric. Estimation of the return levels of rainfall values in Lopburi Province by the Go-GEV distribution indicated that Buachum Station should be monitored because it had higher precipitation and return levels than Lopburi Station at 2, 5, 10 and 15 years. HIGHLIGHTS The analysis of data with extreme values is complex but ignoring an observation just because it is unacceptable is not best practice. One of the widely used tools in such situations is “Extreme Value Theory” The Gompertz-generalized extreme value (Go-GEV) distribution is a new extension of GEV distribution using deffinition of Gompertz-generalized family of distributions The developed Go-GEV model described the maximum rainfall data better than the GEV distribution because the new extension distribution was more flexible and its probability density function had a more diverse shape, such as both left-skewed, right-skewed and close to symmetrical The developed Go-GEV model is a flexible alternative for applying the model to extreme value data GRAPHICAL ABSTRACT

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Lu, Wanbo, and Jyun-You Chiang. "On some life distributions with flexible failure rate." Quality Technology & Quantitative Management 15, no. 3 (September 15, 2016): 413–33. http://dx.doi.org/10.1080/16843703.2016.1226596.

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da Silva, Nívea B., Marcos O. Prates, and Flávio B. Gonçalves. "Bayesian linear regression models with flexible error distributions." Journal of Statistical Computation and Simulation 90, no. 14 (July 2, 2020): 2571–91. http://dx.doi.org/10.1080/00949655.2020.1783261.

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Dahlin, Johan, Adrian Wills, and Brett Ninness. "Sparse Bayesian ARX models with flexible noise distributions." IFAC-PapersOnLine 51, no. 15 (2018): 25–30. http://dx.doi.org/10.1016/j.ifacol.2018.09.085.

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Chipepa, Fastel, Divine Wanduku, and Broderick Olusegun Oluyede. "Half Logistic Odd Weibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications." Afrika Statistika 15, no. 4 (October 1, 2020): 2481–510. http://dx.doi.org/10.16929/as/2020.2481.169.

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A new flexible and versatile generalized family of distributions, namely, half logistic odd Weibull-Topp-Leone-G (HLOW-TL-G) distribution is presented. The distribution can be traced back to the exponentiated-G distribution. We derive the statistical properties of the proposed family of distributions. Maximum likelihood estimates of the HLOW-TL-G family of distributions are also presented. Five special cases of the proposed family are presented. A simulation study and real data applications on one of the special cases are also presented

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Cordeiro, Gaussm, Abdus Saboor, Muhammad Khan, and Serge Provost. "The transmuted generalized modified Weibull distribution." Filomat 31, no. 5 (2017): 1395–412. http://dx.doi.org/10.2298/fil1705395c.

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Canada EM provost@stats.uwo.ca AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM edwin@usp.br KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than related distributions as measured by the Anderson-Darling (A*) and Cram?r-von Mises (W*) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

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Usta, Ilhan, and Yeliz Mert Kantar. "Analysis of some flexible families of distributions for estimation of wind speed distributions." Applied Energy 89, no. 1 (January 2012): 355–67. http://dx.doi.org/10.1016/j.apenergy.2011.07.045.

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Mønness, Erik. "The power-normal distribution: application to forest stands." Canadian Journal of Forest Research 41, no. 4 (April 2011): 707–14. http://dx.doi.org/10.1139/x10-246.

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Foresters have long sought distribution functions capable of modeling a tree distribution that have good fit, yield flexible models, and are easy to use. The power-normal (PN) distribution originates from the inverse Box–Cox transformation and might be proven to fulfill these requirements. The PN has similarities with Johnson’s system-bounded (SB) distribution and can be seen as a contender. The PN is used in this study to fit the frequency distributions of tree diameter and height. PN is flexible in describing different shapes of observed distributions as indicated by the certain areas in the skewness × kurtosis shape plane. The estimation of the parameters using maximum likelihood is straightforward and the resulting numerical properties are desirable. The shapes achieved by PN are very diverse, even though only three parameters are used. Johnson’s SB has four parameters and estimation is often susceptible to numerical problems when fitted by maximum likelihood estimation. Our results indicate that the performance of PN is superior to that of Johnson’s SB, as shown by the Kolmogorov–Smirnov statistic and visual inspection, particularly for fitting tree height distributions.

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Anderson, Simon P., and André de Palma. "Decoupling the CES Distribution Circle with Quality and Beyond: Equilibrium Distributions and the CES-Logit Nexus." Economic Journal 130, no. 628 (February 26, 2020): 911–36. http://dx.doi.org/10.1093/ej/ueaa001.

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Abstract We show for CES demands with heterogeneous productivities that profit, revenue and output distributions lie in the same closed power family as the productivity distribution (e.g., the ‘Pareto circle’). The price distribution lies in the inverse power family. Equilibrium distribution shapes are linked by linear relations between their density elasticities. Introducing product quality decouples the CES circle, and reconciles Pareto price and Pareto sales revenue distributions. We use discrete choice underpinnings to find variable mark-ups for a more flexible demand formulation bridging CES to logit and beyond. For logit demand, exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions.

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Khaled, A. R. A. "Analysis of Heat Transfer Inside Flexible Thin-Film Channels With Nonuniform Height Distributions." Journal of Heat Transfer 129, no. 3 (May 22, 2006): 401–4. http://dx.doi.org/10.1115/1.2430729.

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Heat transfer inside flexible thin-film channels having nonuniform height distributions is analyzed in this work. The terminology “flexible thin film channel” is referred to a thin-film channel having two plates separated by soft elastic seals. The fluidic volume enclosed between the plates can expand due to any increase in the fluid pressure. This expansion which is determined from the height (distance between the plates) distribution is related to the pressure drop and the seals stiffness by applications of force or moment balance laws on the mobile plate. The seals stiffness parameter (S), Peclet number (Pe), dimensionless inlet height (Hi), and the aspect ratio (ε) are found to be the controlling parameters. It is found that flexible thin-film channels with flexible plates produce additional cooling over the cooling effect for those having inflexible plates. The heated plate temperature when plates are flexible is lower than that for the other case by more than 14.8% when Peε<1.0 and Hi=3.0 Moreover, the cooling effect of flexible thin-film channels is found to increase relative to rigid thin-film channels as the S and Peε decrease. Finally, it is recommended to treat flexible thin-film channels as rigid ones when SA>3.45 (inflexible plates case) or SB>10 (flexible plates case).

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Sellers, Kimberly F., Tong Li, Yixuan Wu, and Narayanaswamy Balakrishnan. "A Flexible Multivariate Distribution for Correlated Count Data." Stats 4, no. 2 (April 15, 2021): 308–26. http://dx.doi.org/10.3390/stats4020021.

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Multivariate count data are often modeled via a multivariate Poisson distribution, but it contains an underlying, constraining assumption of data equi-dispersion (where its variance equals its mean). Real data are oftentimes over-dispersed and, as such, consider various advancements of a negative binomial structure. While data over-dispersion is more prevalent than under-dispersion in real data, however, examples containing under-dispersed data are surfacing with greater frequency. Thus, there is a demonstrated need for a flexible model that can accommodate both data types. We develop a multivariate Conway–Maxwell–Poisson (MCMP) distribution to serve as a flexible alternative for correlated count data that contain data dispersion. This structure contains the multivariate Poisson, multivariate geometric, and the multivariate Bernoulli distributions as special cases, and serves as a bridge distribution across these three classical models to address other levels of over- or under-dispersion. In this work, we not only derive the distributional form and statistical properties of this model, but we further address parameter estimation, establish informative hypothesis tests to detect statistically significant data dispersion and aid in model parsimony, and illustrate the distribution’s flexibility through several simulated and real-world data examples. These examples demonstrate that the MCMP distribution performs on par with the multivariate negative binomial distribution for over-dispersed data, and proves particularly beneficial in effectively representing under-dispersed data. Thus, the MCMP distribution offers an effective, unifying framework for modeling over- or under-dispersed multivariate correlated count data that do not necessarily adhere to Poisson assumptions.

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Shama, Mustafa S., Farid El Ktaibi, Jamal N. Al Abbasi, Christophe Chesneau, and Ahmed Z. Afify. "Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions." Axioms 12, no. 1 (January 7, 2023): 67. http://dx.doi.org/10.3390/axioms12010067.

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In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model.

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Abu El Azm, Wael S., Ehab M. Almetwally, Sundus Naji AL-Aziz, Abd Al-Aziz H. El-Bagoury, Randa Alharbi, and O. E. Abo-Kasem. "A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID-19 Data." Computational Intelligence and Neuroscience 2021 (October 7, 2021): 1–14. http://dx.doi.org/10.1155/2021/5918511.

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A new five-parameter transmuted generalization of the Lomax distribution (TGL) is introduced in this study which is more flexible than current distributions and has become the latest distribution theory trend. Transmuted generalization of Lomax distribution is the name given to the new model. This model includes some previously unknown distributions. The proposed distribution's structural features, closed forms for an rth moment and incomplete moments, quantile, and Rényi entropy, among other things, are deduced. Maximum likelihood estimate based on complete and Type-II censored data is used to derive the new distribution's parameter estimators. The percentile bootstrap and bootstrap-t confidence intervals for unknown parameters are introduced. Monte Carlo simulation research is discussed in order to estimate the characteristics of the proposed distribution using point and interval estimation. Other competitive models are compared to a novel TGL. The utility of the new model is demonstrated using two COVID-19 real-world data sets from France and the United Kingdom.

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Ghitany, M. E., and Samuel Kotz. "RELIABILITY PROPERTIES OF EXTENDED LINEAR FAILURE-RATE DISTRIBUTIONS." Probability in the Engineering and Informational Sciences 21, no. 3 (July 2007): 441–50. http://dx.doi.org/10.1017/s0269964807000071.

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This article investigates reliability properties of a flexible extended linear failure-rate family of distributions generated using the relation F¯(x) = αF¯0(x)/[1 − α¯F¯0(x)], where α > 0, α¯ = 1 − α, and F¯0(x) is the reliability function of the linear failure-rate distribution.

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44

Eliwa, Mohamed S., Fahad Sameer Alshammari, Khadijah M. Abualnaja, and Mahmoud El-Morshedy. "A Flexible Extension to an Extreme Distribution." Symmetry 13, no. 5 (April 23, 2021): 745. http://dx.doi.org/10.3390/sym13050745.

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The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

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45

Abdul Majid, Muhammad Hilmi, and Kamarulzaman Ibrahim. "Composite Pareto Distributions for Modelling Household Income Distribution in Malaysia." Sains Malaysiana 50, no. 7 (July 31, 2021): 2047–58. http://dx.doi.org/10.17576/jsm-2021-5007-19.

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Composite Pareto distributions are flexible as the models allow for data to be described by two distributions: a Pareto distribution for the data above a threshold value and another separate distribution for data below the threshold value. It is noted in some previous literatures that the Paretian tail behaviour can be observed in the distribution of Malaysian household income. In this paper, the composite Pareto models are fitted to the Malaysian household income data of several years. These fitted composite Pareto models are then compared to several univariate models for describing income distribution using pseudo-likelihood based AIC, BIC and Kolmogorov-Smirnov goodness-of-fit test. It is found that the income distributions in Malaysia can be best described by the lognormal-Pareto (II) model as compared to other candidate models.

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46

Hout, Ardo van den, and Wenhui Tan. "Flexible parametric multistate modelling of employment history." Statistical Modelling 19, no. 3 (June 2019): 323–38. http://dx.doi.org/10.1177/1471082x19836299.

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A multistate model is used to describe employment history. Transition-specific rates are defined using generalized gamma distributions and Gompertz distributions. This flexible parametric modelling of the rate of change is combined with latent classes for unobserved propensity to change jobs. The propensity is described by two latent classes which can be interpreted as consisting of movers and stayers. The modelling is illustrated by analysing longitudinal data from the German Life History Study.

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47

Alhassan, Abukari. "Gompertz Ampadu Class of Distributions: Properties and Applications." Journal of Probability and Statistics 2022 (April 20, 2022): 1–7. http://dx.doi.org/10.1155/2022/1104330.

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This paper introduces a new generator family of distributions called the Gompertz Ampadu-G family. Based on the generator, the Lomax distribution was modified into Gompertz Ampadu Lomax. The new distribution has a flexible hazard rate function that has upside-down and bathtub shapes, including increasing and decreasing hazard rate functions. The distribution comes with some desirable statistical properties. The distribution is applied to real-life data. Parameter estimates and test statistics show a better fit for the competitive models.

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48

KUBRAK, ELŻBIETA, JANUSZ KUBRAK, and PAWEŁ M. ROWIŃSKI. "Vertical velocity distributions through and above submerged, flexible vegetation." Hydrological Sciences Journal 53, no. 4 (August 2008): 905–20. http://dx.doi.org/10.1623/hysj.53.4.905.

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49

Ohkawa, Hideo. "Stress Distributions around Buried Flexible Conduits under Earth Loads." Soils and Foundations 27, no. 4 (December 1987): 167–75. http://dx.doi.org/10.3208/sandf1972.27.4_167.

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50

Rocha, Gustavo H. M. A., Rosangela H. Loschi, and Reinaldo B. Arellano-Valle. "Inference in flexible families of distributions with normal kernel." Statistics 47, no. 6 (December 2013): 1184–206. http://dx.doi.org/10.1080/02331888.2012.688207.

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