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Journal articles on the topic 'Weibull distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 February 2023

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1

Oluyede, Broderick. "The Gamma-Weibull-G Family of Distributions with Applications." Austrian Journal of Statistics 47, no. 1 (January 30, 2018): 45–76. http://dx.doi.org/10.17713/ajs.v47i1.155.

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Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-WeibullG family of distributions (GWG). Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. We also present R´enyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data

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2

Alzoubi, Loai, Ahmad Al-Khazaleh, Ayat Al-Meanazel, and Mohammed Gharaibeh. "EPANECHNIKOV-WEIBULL DISTRIBUTION." Journal of Southwest Jiaotong University 57, no. 6 (December 30, 2022): 949–58. http://dx.doi.org/10.35741/issn.0258-2724.57.6.81.

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The idea of using kernel functions combined with distributions to propose new distributions has recently been used to suggest new continuous distributions. This article combined the Epanechnikov kernel function with the Weibull distribution to produce the Epanechnikov-Weibull distribution (EWD). We have presented some properties of EWD, like the moments, MLEs, reliability analysis functions, Rényi entropy and the quantile function. We estimated the model parameters using the maximum likelihood method. A simulation study was conducted to calculate the MLE in terms of biases, mean square errors and mean relative, it shows that the estimates are consistent. Two real data set applications revealed that EWD is more flexible than the Weibull distribution.

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3

Cao, Quang V., and Qinglin Wu. "Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution." Holzforschung 61, no. 2 (March 1, 2007): 124–30. http://dx.doi.org/10.1515/hf.2007.023.

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Abstract The length data from 12 samples of wood fibers and particles were described using lognormal and Weibull distributions. While both distributions fitted the middle range of the data well, the lognormal distribution provided a closer fit for short fibers and particles and the Weibull distribution was more appropriate for long ones. A mixture of the lognormal and Weibull distributions was developed using a variable weight to allow the new distribution to take the lognormal form for short fibers and gradually change to the Weibull form for long fibers. In the segmented distribution approach, a left segment of the lognormal distribution was joined to a right segment from the Weibull form. The Anderson-Darling goodness-of-fit test at the 5% level failed to reject the hypothesis that the mixture distribution and the segmented distribution fitted the data. Q-Q plots showed that both the mixture and segmented distributions provided an excellent fit to the fiber and particle length data, combining the best features of the lognormal and the Weibull distributions. These two new distributions are therefore better alternatives than the single lognormal and Weibull distributions for this data set.

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4

Almazah, Mohammed M. A., Kalim Ullah, Eslam Hussam, Md Moyazzem Hossain, Ramy Aldallal, and Fathy H. Riad. "New Statistical Approaches for Modeling the COVID-19 Data Set: A Case Study in the Medical Sector." Complexity 2022 (August 19, 2022): 1–9. http://dx.doi.org/10.1155/2022/1325825.

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Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution.

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5

Kızılersü, Ayşe, Markus Kreer, and Anthony W. Thomas. "The Weibull distribution." Significance 15, no. 2 (April 2018): 10–11. http://dx.doi.org/10.1111/j.1740-9713.2018.01123.x.

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6

Mustafa, Abdelfattah, Beih S. Desouky, and Shamsan AL-Garash. "THE WEIBULL GENERALIZED FLEXIBLE WEIBULL EXTENSION DISTRIBUTION." Journal of Data Science 14, no. 3 (March 5, 2021): 453–78. http://dx.doi.org/10.6339/jds.201607_14(3).0004.

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7

Klakattawi, Hadeel S. "The Weibull-Gamma Distribution: Properties and Applications." Entropy 21, no. 5 (April 26, 2019): 438. http://dx.doi.org/10.3390/e21050438.

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A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

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8

Aminu Adamu, Abubakar Yahaya, and Hussaini Garba Dikko. "APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS." FUDMA JOURNAL OF SCIENCES 5, no. 2 (June 22, 2021): 89–99. http://dx.doi.org/10.33003/fjs-2021-0502-479.

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In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

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9

Makubate, Boikanyo, Broderick O. Oluyede, Gofaone Motobetso, Shujiao Huang, and Adeniyi F. Fagbamigbe. "The Beta Weibull-G Family of Distributions: Model, Properties and Application." International Journal of Statistics and Probability 7, no. 2 (January 18, 2018): 12. http://dx.doi.org/10.5539/ijsp.v7n2p12.

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A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

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10

Jain, Kanchan, Neetu Singla, and Suresh Kumar Sharma. "The Generalized Inverse Generalized Weibull Distribution and Its Properties." Journal of Probability 2014 (August 6, 2014): 1–11. http://dx.doi.org/10.1155/2014/736101.

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The Inverse Weibull distribution has been applied to a wide range of situations including applications in medicine, reliability, and ecology. It can also be used to describe the degradation phenomenon of mechanical components. We introduce Inverse Generalized Weibull and Generalized Inverse Generalized Weibull (GIGW) distributions. GIGW distribution is a generalization of several distributions in literature. The mathematical properties of this distribution have been studied and the mixture model of two Generalized Inverse Generalized Weibull distributions is investigated. Estimates of parameters using method of maximum likelihood have been computed through simulations for complete and censored data.

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11

Smadi, Mahmoud M., and Mahmoud H. Alrefaei. "New extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 6 (December 1, 2021): 5107. http://dx.doi.org/10.11591/ijece.v11i6.pp5107-5118.

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The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.

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12

Oluyede, Broderick, Shujiao Huang, and Tiantian Yang. "A New Class of Generalized Modified Weibull Distribution with Applications." Austrian Journal of Statistics 44, no. 3 (October 14, 2015): 45–68. http://dx.doi.org/10.17713/ajs.v44i3.36.

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A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

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13

Zamanah, Ernest, Suleman Nasiru, and Albert Luguterah. "Harmonic Mixture Weibull-G Family of Distributions: Properties, Regression and Applications to Medical Data." Computational and Mathematical Methods 2022 (November 28, 2022): 1–24. http://dx.doi.org/10.1155/2022/2836545.

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In recent years, the developments of new families of probability distributions have received greater attention as a result of desirable properties they exhibit in the modelling of data sets. The Harmonic Mixture Weibull-G family of distributions was developed in this study. The statistical properties were comprehensively presented and five special distributions developed from the family. The hazard functions of the special distributions were shown to exhibit various forms of monotone and nonmonotone shapes. The applications of the developed family to real data sets in medical studies revealed that the special distribution (Harmonic mixture Weibul Weibull distribution) provided a better fit to the data sets than other competitive models. A location-scale regression model was developed from the family and its application demonstrated using survival time data of hypertensive patients.

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14

Tizgui, Ijjou, Fatima El Guezar, Hassane Bouzahir, and Brahim Benaid. "Wind speed distribution modeling for wind power estimation: Case of Agadir in Morocco." Wind Engineering 43, no. 2 (June 4, 2018): 190–200. http://dx.doi.org/10.1177/0309524x18780391.

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To estimate a wind turbine output, optimize its dimensioning, and predict the economic profitability and risks of a wind energy project, wind speed distribution modeling is crucial. Many researchers use directly Weibull distribution basing on a priori acceptance. However, Weibull does not fit some wind speed regimes. The goal of this work is to model the wind speed distribution at Agadir. For that, we compare the accuracy of four distributions (Weibull, Rayleigh, Gamma, and lognormal) which have given good results in this yield. The goodness-of-fit tests are applied to select the effective distribution. The obtained results explain that Weibull distribution is fitting the histogram of observations better than the other distributions. The analysis deals with comparing the error in estimating the annual wind power density using the examined distributions. It was found that Weibull distribution presents minimum error. Thus, wind energy assessors in Agadir can use directly Weibull distribution basing on a scientific decision made via statistical tests. Moreover, assessors worldwide can use the followed methodology to model their wind speed measurements.

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15

Srisaila, A., D. Rajani, M. V. D. N. S. Madhavi, G. Jaya Lakshmi, K. Amarendra, and Narasimha Rao Dasari. "An Improved Data Generalization Model for Real-Time Data Analysis." Scientific Programming 2022 (August 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/4118371.

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This research proposes a maximum likelihood-Weibull distribution (WD) model for the generalized data distribution family. The distribution function of the anticipated maximum likelihood-Weibull distribution is defined where the statistical properties are derived. The data distribution is capable of modelling monotonically decreasing, increasing, and constant hazard rates. The proposed maximum likelihood-Weibull distribution is used for evaluated these parameters. The experimentation is done to evaluate the potential of the maximum likelihood-Weibull distribution estimated. Here, the online available dataset is adopted for computing the anticipated maximum likelihood-Weibull distribution performance. The outcomes show that the anticipated model is well-suited for computation and compared with other distributions as it possesses maximal and least value of some statistical criteria.

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16

Deng, Bin, Xingang Wang, Danyu Jiang, and Jianghong Gong. "Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution." Processing and Application of Ceramics 14, no. 4 (2020): 293–302. http://dx.doi.org/10.2298/pac2004293d.

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It is generally assumed that the measured strength of brittle ceramics follows a Weibull distribution. However, there seems to be few sound and direct evidences to support this assumption. Several previous studies have shown that other distributions, such as normal distribution and log-normal distribution may describe more appropriately the strength data than Weibull distribution. In this paper, the efficiency of using a normal distribution to describe the strength which follows a Weibull distribution is examined based on Monte-Carlo simulations. It was shown that there exist strong correlations between the parameters of normal distribution and those of Weibull distribution. For the designed fracture probability not lower than 0.01, analyses based on both normal distribution and Weibull distribution may give nearly identical predictions for the applicable stress levels. For lower fracture probabilities, the differences between the predictions of both distributions are not significant. It was suggested that, if there is no evidence to confirm that the measured strength follows a certain distribution, normal distribution and Weibull distribution seem to have the same efficiency in analysing the statistical variations in the measured strength of ceramics.

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17

Deng, Bin, Xingang Wang, Danyu Jiang, and Jianghong Gong. "Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution." Processing and Application of Ceramics 14, no. 4 (2020): 293–302. http://dx.doi.org/10.2298/pac2004293d.

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It is generally assumed that the measured strength of brittle ceramics follows a Weibull distribution. However, there seems to be few sound and direct evidences to support this assumption. Several previous studies have shown that other distributions, such as normal distribution and log-normal distribution may describe more appropriately the strength data than Weibull distribution. In this paper, the efficiency of using a normal distribution to describe the strength which follows a Weibull distribution is examined based on Monte-Carlo simulations. It was shown that there exist strong correlations between the parameters of normal distribution and those of Weibull distribution. For the designed fracture probability not lower than 0.01, analyses based on both normal distribution and Weibull distribution may give nearly identical predictions for the applicable stress levels. For lower fracture probabilities, the differences between the predictions of both distributions are not significant. It was suggested that, if there is no evidence to confirm that the measured strength follows a certain distribution, normal distribution and Weibull distribution seem to have the same efficiency in analysing the statistical variations in the measured strength of ceramics.

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18

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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19

Darwish, Jumanah Ahmed, Saman Hanif Shahbaz, Lutfiah Ismail Al-Turk, and Muhammad Qaiser Shahbaz. "Some bivariate and multivariate families of distributions: Theory, inference and application." AIMS Mathematics 7, no. 8 (2022): 15584–611. http://dx.doi.org/10.3934/math.2022854.

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<abstract> <p>The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used.</p> </abstract>

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20

Mabel, Y. O., M. Novita, and S. Nurrohmah. "Discrete Weibull-geometric distribution." Journal of Physics: Conference Series 1725 (January 2021): 012033. http://dx.doi.org/10.1088/1742-6596/1725/1/012033.

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21

Sewilanl, Eman M. "Generalized Weibull Distribution Revisited." المجلة العلمیة للبحوث التجاریة 14, no. 2 (October 1, 2008): 8–25. http://dx.doi.org/10.21608/sjsc.2008.118642.

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22

Ahmad, Zubair, and Zawar Hussain. "New Extended Weibull Distribution." Circulation in Computer Science 2, no. 6 (July 20, 2017): 14–19. http://dx.doi.org/10.22632/ccs-2017-252-31.

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This article considers a new function to propose a new lifetime model. The new model is introduced by utilizing the linear scheme of the two logarithms of cumulative hazard functions. The new model is named as new extended Weibull distribution, and is able to model data with unimodal or modified unimodal shaped failure rates. A brief explanation of the mathematical properties of the proposed model is provided. The model parameters will be estimated by deploying the maximum likelihood method. To illustrate the usefulness of the proposed model, an example will be discussed.

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23

Lee, Cheng, and Miin-Jye Wen. "A MULTIVARIATE WEIBULL DISTRIBUTION." Pakistan Journal of Statistics and Operation Research 5, no. 2 (July 30, 2010): 55. http://dx.doi.org/10.18187/pjsor.v5i2.120.

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24

ALWAKEEL, ALI HUSEEN. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (October 1, 2014): 1–9. http://dx.doi.org/10.33095/jeas.v20i79.1969.

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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obtained as the discrete counterparts of either the distribution function or the failure rate function of the standard Weibull model. Which lead to different models. This paper discusses the discrete model which is the counterpart of the standard two-parameter Weibull distribution. It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.

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25

الوكيل, علي عبد الحسين. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (October 1, 2014): 1. http://dx.doi.org/10.33095/jeas.v20i79.807.

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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assume the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables takes on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obtained as the discrete counter parts of either the distribution function or the failure rate function of the standard Weibull model. Which lead to different models. This paper discusses the discrete model which is the counter part of the standard two-parameter Weibull distribution. It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.

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26

Barreto-Souza, Wagner, Alice Lemos de Morais, and Gauss M. Cordeiro. "The Weibull-geometric distribution." Journal of Statistical Computation and Simulation 81, no. 5 (May 2011): 645–57. http://dx.doi.org/10.1080/00949650903436554.

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Muhammed, Hiba Z. "Bivariate inverse Weibull distribution." Journal of Statistical Computation and Simulation 86, no. 12 (November 8, 2015): 2335–45. http://dx.doi.org/10.1080/00949655.2015.1110585.

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28

Gupta, Jaya, and Mridula Garg. "The Lomax-Weibull Distribution." Advanced Science Letters 24, no. 11 (November 1, 2018): 8126–29. http://dx.doi.org/10.1166/asl.2018.12506.

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29

Khan, Muhammad Shuaib, and Robert King. "Modified Inverse Weibull Distribution." Journal of Statistics Applications & Probability 1, no. 2 (July 1, 2012): 115–32. http://dx.doi.org/10.12785/jsap/010204.

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Lai, C. D., M. Xie, and D. N. P. Murthy. "A modified Weibull distribution." IEEE Transactions on Reliability 52, no. 1 (March 2003): 33–37. http://dx.doi.org/10.1109/tr.2002.805788.

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31

Ahmad, Abd EL-Baset A., and M. G. M. Ghazal. "Exponentiated additive Weibull distribution." Reliability Engineering & System Safety 193 (January 2020): 106663. http://dx.doi.org/10.1016/j.ress.2019.106663.

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32

Shafaei Nooghabi, Mohamad, Gholam Reza Mohtashami Borzadaran, and Abdol Hamid Rezaei Roknabadi. "Discrete modified Weibull distribution." METRON 69, no. 2 (August 2011): 207–22. http://dx.doi.org/10.1007/bf03263557.

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33

Karina, Tania M., Siti Nurrohmah, and Ida Fithriani. "Heterogeneous Weibull count distribution." Journal of Physics: Conference Series 1218 (May 2019): 012020. http://dx.doi.org/10.1088/1742-6596/1218/1/012020.

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Khan, Muhammad Nauman, Anwaar Saeed, and Ayman Alzaatreh. "Weighted Modified Weibull Distribution." Journal of Testing and Evaluation 47, no. 5 (October 9, 2018): 20170370. http://dx.doi.org/10.1520/jte20170370.

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35

Jayakumar, K., and K. K. Sankaran. "Discrete Linnik Weibull distribution." Communications in Statistics - Simulation and Computation 48, no. 10 (October 27, 2018): 3092–117. http://dx.doi.org/10.1080/03610918.2018.1475009.

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36

El-Morshedy, Mahmoud, Zahra Almaspoor, Nasir Abbas, and Zahid Khan. "A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector." Mathematical Problems in Engineering 2022 (August 8, 2022): 1–12. http://dx.doi.org/10.1155/2022/8569332.

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The Weibull distribution has prominent applications in the engineering sector. However, due to its monotonic behavior of the hazard function, the Weibull model does not provide the best fit for data in many cases. This paper introduces a new family of distributions to obtain new flexible distributions. The proposed family is called a novel generalized- M family. Based on this approach, an updated version of the Weibull distribution is introduced. The updated version of the Weibull distribution is called a novel generalized Weibull distribution. The proposed distribution is able to capture four different patterns of the hazard function. Some mathematical properties of the proposed method are obtained. Furthermore, the maximum likelihood estimators of the proposed family are also obtained. Moreover, a simulation study is conducted for evaluating these estimators. For illustrating the proposed model, two data sets from the engineering sector are analyzed. Based on some well-known analytical measures, it is shown that the novel generalized Weibull distribution is the best competing distribution for analyzing the engineering data sets.

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37

sadani, Sahar, Kamel abdollahnezhad, mahdi teimouri, and Vahid ranjbar. "New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution." Journal of Statistical Research of Iran 16, no. 1 (September 1, 2019): 33–57. http://dx.doi.org/10.52547/jsri.16.1.33.

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Ortega, Edwin Moises Marcos, Fábio Prataviera, and Gauss Moutinho Cordeiro. "Four generalized Weibull distributions: similar properties and applications." Ciência e Natura 42 (September 3, 2020): e10. http://dx.doi.org/10.5902/2179460x40100.

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We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation.

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39

Tumidajski, P. J., L. Fiore, T. Khodabocus, M. Lachemi, and R. Pari. "Comparison of Weibull and normal distributions for concrete compressive strengths." Canadian Journal of Civil Engineering 33, no. 10 (October 1, 2006): 1287–92. http://dx.doi.org/10.1139/l06-080.

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For concrete produced in a commercial ready mix operation, the compressive strengths were fitted to Weibull and normal distributions. It was found that the Weibull distribution successfully describes concrete compressive strength failure data. This information is useful in the theoretical description of concrete failure. Furthermore, based on chi-squared, Anderson–Darling and Kolmogorov-Smirnov goodness-of-fit tests, the difference between the Weibull and normal distribution is not large enough to make a clear distinction regarding which distribution definitively fits the experimental data better. Key words: compressive strength, normal distribution, Weibull distribution, goodness-of-fit.

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40

Braimah, J. O., J. A. Adjekukor, N. Edike, and S. O. Elakhe. "A new Weibull Exponentiated Inverted Weibull Distribution for modelling positively-skewed data." Global Journal of Pure and Applied Sciences 27, no. 1 (March 5, 2021): 43–53. http://dx.doi.org/10.4314/gjpas.v27i1.6.

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An Exponentiated Inverted Weibull Distribution (EIWD) has a hazard rate (failure rate) function that is unimodal, thus making it less efficient for modeling data with an increasing failure rate (IFR). Hence, the need to generalize the EIWD in order to obtain a distribution that will be proficient in modeling these types of dataset (data with an increasing failure rate). This paper therefore, extends the EIWD in order to obtain Weibull Exponentiated Inverted Weibull (WEIW) distribution using the Weibull-Generator technique. Some of the properties investigated include the mean, variance, median, moments, quantile and moment generating functions. The explicit expressions were derived for the order statistics and hazard/failure rate function. The estimation of parameters was derived using the maximum likelihood method. The developed model was applied to a real-life dataset and compared with some existing competing lifetime distributions. The result revealed that the (WEIW) distribution provided a better fit to the real life dataset than the existing Weibull/Exponential family distributions.

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Alizadeh, Morad, Muhammad Nauman Khan, Mahdi Rasekhi, and G.G Hamedani. "A New Generalized Modified Weibull Distribution." Statistics, Optimization & Information Computing 9, no. 1 (January 22, 2021): 17–34. http://dx.doi.org/10.19139/soic-2310-5070-1014.

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We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer's $G$--function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness--of--fit tests

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Salsinha, Cecilia Novianti. "Estimasi Parameter Distribusi Weibull Dan Aplikasinya pada Pengendalian Mutu Dengan Memanfaatkan Kuantil." Unisda Journal of Mathematics and Computer Science (UJMC) 5, no. 01 (June 13, 2019): 9–15. http://dx.doi.org/10.52166/ujmc.v5i01.1473.

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Abstract. Weibull distribution is one of the continuous probability distributions. As the other distributions, Weibull distribution is also characterized by Mean, Variance and Moment Generation Function. The advantage of this distribution compared to other distributions is its flexibility, that is, this distribution can change to another distribution such as an exponential distribution depending on the value of the selected distribution parameters, namely scale parameters and form parameters. From the distribution graph, it can be shown that, the flexibility will appear very clear. One application of the Weibull distribution is in statistical process control. Because not all data is normally distributed, the Shewhart control chart cannot be used. One way to solve this problem is that the data is analyzed with Weibull control charts by utilizing quantiles, namely 0.00135, 0.5 and 0.99865. Quantile 0.00135 is the bottom quintile used to form the Lower Control Limit, the Middle Line is the median of the data, which is 0.5 which replaces the average and the last to form the Upper Control Limit the top quintile is 0.99865. By generating 200 data with Weibull distribution, if the data is analyzed by Shewhart control charts then there is a lot of data that is outside the control limit so it will be concluded that the graph is out of control. Therefore, if the data is not from a Normal distribution, the use of Shewhart control charts is not recommended. Keywords: Weibull Distribution, Maximum Likelihood Estimation (MLE), Quality Control, Weibull Control Charts Abstrak. Distribusi Weibull merupakan salah satu distribusi probabilitas kontinu. Sama halnya dengan distribusi lainnya, distribusi Weibull pun dicirikan dengan Mean, Variansi dan Fungsi Pembangkit Momen. Kelebihan distribusi ini dibandingkan dengan distribusi lainnya adalah fleksibilitasnya, yaitu distribusi ini dapat berubah menjadi distribusi lain seperti distribusi eksponensial tergantung pada nilai parameter distribusi yang dipilih yaitu parameter skala dan parameter bentuk. Jika dilihat dari grafik distribusinya maka akan tampak sangat jelas fleksibilitas tersebut. Salah satu aplikasi dari distribusi Weibull yaitu dalam pengendalian proses statistik. Oleh karena tidak semua data berdistribusi normal maka grafik pengendali Shewhart tidak dapat digunakan. Salah satu cara menyelesaikan masalah tersebut adalah data dianalisis dengan grafik pengendali Weibull dengan memanfaatkan kuantil-kuantil yaitu 0,00135, 0,5 dan 0,99865. Kuantil 0,00135 adalah kuantil bawah yang digunakan untuk membentuk Batas Pengendali Bawah, Garis Tengah adalah median dari data yaitu 0,5 yang menggantikan rata-rata dan untuk membentuk Batas Pengendali Atas digunakan kuantil atas yaitu 0,99865. Dengan membangkitkan data sebanyak 200 data berdistribusi Weibull, jika data tersebut dianalisis dengan grafik pengendali Shewhart maka terdapat banyak data yang berada diluar batas pengendali sehingga akan disimpulkan bahwa grafik tak terkendali. Oleh karena itu, jika data bukan berasal dari distribusi Normal, penggunaan grafik pengendali Shewhart tidak disarankan. Kata Kunci: Distribusi Weibull, Estimasi Maximum Likelihood, Pengendalian Mutu, Grafik Pengendali Weibull

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Alyami, Salem A., Ibrahim Elbatal, Naif Alotaibi, Ehab M. Almetwally, Hassan M. Okasha, and Mohammed Elgarhy. "Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data." Applied Sciences 12, no. 20 (October 16, 2022): 10431. http://dx.doi.org/10.3390/app122010431.

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In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions.

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Shahzad, Mirza Naveed, Ehsan Ullah, and Abid Hussanan. "Beta Exponentiated Modified Weibull Distribution: Properties and Application." Symmetry 11, no. 6 (June 12, 2019): 781. http://dx.doi.org/10.3390/sym11060781.

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One of the most prominent statistical distributions is the Weibull distribution. The recent modifications in this distribution have enhanced its application but only in specific fields. To introduce a more generalized Weibull distribution, in this work beta exponentiated modified Weibull distribution is established. This distribution consolidate the exponential, skewed and symmetric shapes into one density. The proposed distribution also contains nineteen lifetime distributions as a special case, which shows the flexibility of the distribution. The statistical properties of the proposed model are derived and discussed, including reliability analysis and order statistics. The hazard function of the proposed distribution can have a unimodal, decreasing, bathtub, upside-down bathtub, and increasing shape that make it effective in reliability analysis. The parameters of the proposed model are evaluated by maximum likelihood and least squares estimation methods. The significance of the beta exponentiated modified Weibull distribution for modeling is illustrated by the study of real data. The numerical study indicates that the new proposed distribution gives better results than other comparable distributions.

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45

Oluyede, Broderick, Precious Mdlongwa, Boikanyo Makubate, and Shujiao Huang. "The Burr-Weibull Power Series Class of Distributions." Austrian Journal of Statistics 48, no. 1 (December 17, 2018): 1–13. http://dx.doi.org/10.17713/ajs.v48i1.633.

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A new generalized class of distributions called the Burr-Weibull Power Series (BWPS) class of distributions is developed and explored. This class of distributions generalizes the Burr power series and Weibull power series classes of distributions, respectively. A special model of the BWPS class of distributions, the new Burr-Weibull Poisson (BWP) distribution is considered and some of its mathematical properties are obtained. The BWP distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential Poisson, Burr-exponential, Burr-Rayleigh Poisson, Burr-Rayleigh, Burr-Poisson, Burr, Lomax-exponential Poisson, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax-Poisson, Lomax, Weibull, Rayleigh and exponential distributions. Maximum likelihood estimation technique is used to estimate the model parameters followed by a Monte Carlo simulation study. Finally an application of the BWP model to a real data set is presented to illustrate the usefulness of the proposed class of distributions.

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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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Cooray, Kahadawala. "Generalization of the Weibull distribution: the odd Weibull family." Statistical Modelling: An International Journal 6, no. 3 (October 2006): 265–77. http://dx.doi.org/10.1191/1471082x06st116oa.

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48

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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Pogány, Tibor, and Abdus Saboor. "The gamma exponentiated exponential-Weibull distribution." Filomat 30, no. 12 (2016): 3159–70. http://dx.doi.org/10.2298/fil1612159p.

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Anewfour-parameter model called the gamma-exponentiated exponential-Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson-Darling and Cram?r-von Mises goodness-of-fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

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CHEN, ZHENMIN. "EXACT CONFIDENCE INTERVALS AND JOINT CONFIDENCE REGIONS FOR THE PARAMETERS OF THE WEIBULL DISTRIBUTIONS." International Journal of Reliability, Quality and Safety Engineering 11, no. 02 (June 2004): 133–40. http://dx.doi.org/10.1142/s0218539304001403.

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The Weibull distribution is widely adopted as a lifetime distribution. One of the characteristics the Weibull distribution possesses is that its cumulative distribution function can be expressed by closed form. Parameter estimation for the Weibull distribution has been discussed by many authors. Various methods have been proposed for constructing confidence intervals and joint confidence regions for the parameters of the Weibull distribution based on censored data. This paper discusses those methods that deal with exact confidence intervals or exact joint confidence regions for the parameters. One of the applications of the joint confidence regions of the parameters is to find confidence bounds for the functions of the parameters. In this paper, confidence bounds for the mean lifetime and reliability function for the Weibull distributions are discussed. Some unresolved problems for the exact confidences and joint confidence regions are mentioned in the discussion section.

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