The Weibull-Gamma Distribution: Properties and Applications

Klakattawi, Hadeel S.

doi:10.3390/e21050438

Cited by 26 publications

(12 citation statements)

References 26 publications

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“…Many studies have been considered of some members of the Weibull-G family, such as the Weibull-Pareto by [ 27 ], the Weibull-Rayleigh by [ 28 ], the Weibull-Lomax by [ 29 ] and more lately the Weibull-gamma by [ 30 ].…”

Section: Introductionmentioning

confidence: 99%

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

Klakattawi¹,

Alsulami²,

Elaal³

et al. 2022

PLoS ONE

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Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

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Section: Introductionmentioning

confidence: 99%

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

Klakattawi¹,

Alsulami²,

Elaal³

et al. 2022

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…The classical Weibull-G class has been successfully applied to several significant disciplines in recent years, including medical, biology, engineering, dependability, economics, computer science, and finance. Detailed examples can be found in [5,35,36], among others. Our new Weibull-generated class can be used in similar scenarios.…”

Section: Discussionmentioning

confidence: 99%

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

Hussain

Chesneau

2021

MCA

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In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best.

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“…The third application considers the data set obtained from [17]. It gives the failure and running times of a sample of 30 devices, and are studied by [14], among others. The data set is given by: We also adopt the models studied in [14] as competitive models.…”

Section: Third Applicationmentioning

confidence: 99%

“…It gives the failure and running times of a sample of 30 devices, and are studied by [14], among others. The data set is given by: We also adopt the models studied in [14] as competitive models. In Table 7, we compare the MOW-gamma model with these competitive models, by comparing their AIC statistics.…”

Section: Third Applicationmentioning

confidence: 99%

Modified Odd Weibull Family of Distributions: Properties and Applications

Chesneau

Achi

2020

J Indian Soc Probab Stat

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In this paper, a new family of continuous distributions, called the modified odd Weibull-G (MOW-G) family, is studied. The MOW-G family has the feature to use the Weibull distribution as main generator and a new modification of the odd transformation, opening new horizon in terms of statistical modelling. Its main theoretical and practical aspects are explored. In particular, for the mathematical properties, we investigate some results in distribution, quantile function, skewness, kurtosis, moments, moment generating function, order statistics and entropy. For the statistical aspect, the maximum likelihood estimation method is used to estimate the model parameters. The performance of this method is evaluated by a Monte Carlo simulation study. Applications to three practical data sets are given to demonstrate the usefulness of the MOW-G model.

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The Weibull-Gamma Distribution: Properties and Applications

Cited by 26 publications

References 26 publications

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

Modified Odd Weibull Family of Distributions: Properties and Applications

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