An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications

doi:10.1007/s42967-021-00167-w

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1229-1257.doi: 10.1007/s42967-021-00167-w

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An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications

Christophe Chesneau¹, Kadir Karakaya², Hassan S. Bakouch³, Coşkun Kuş²

1. LMNO, Université de Caen, Campus II, Science 3, 14032, Caen, France;
2. Department of Statistics, Faculty of Science, Selçuk University, 42250, Konya, Turkey;
3. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

收稿日期:2021-04-01 修回日期:2021-07-29 出版日期:2022-12-20 发布日期:2022-09-26
通讯作者: Kadir Karakaya,E-mail:kkarakaya@selcuk.edu.tr;Christophe Chesneau,E-mail:christophe.chesneau@unicaen.fr;Hassan S. Bakouch,E-mail:hassan.bakouch@science.tanta.edu.eg;Coşkun Kuş,E-mail:coskun@selcuk.edu.tr E-mail:kkarakaya@selcuk.edu.tr;christophe.chesneau@unicaen.fr;hassan.bakouch@science.tanta.edu.eg;coskun@selcuk.edu.tr
基金资助:
We would like to express our gratitude to the reviewers for their time and work in helping us to improve our manuscript.

An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications

Christophe Chesneau¹, Kadir Karakaya², Hassan S. Bakouch³, Coşkun Kuş²

1. LMNO, Université de Caen, Campus II, Science 3, 14032, Caen, France;
2. Department of Statistics, Faculty of Science, Selçuk University, 42250, Konya, Turkey;
3. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Received:2021-04-01 Revised:2021-07-29 Online:2022-12-20 Published:2022-09-26
Supported by:
We would like to express our gratitude to the reviewers for their time and work in helping us to improve our manuscript.

摘要/Abstract

摘要： This paper introduces a new rich family of distributions based on mixtures and the so-called Marshall-Olkin family of distributions. It includes a wide variety of well-established mixture distributions, ensuring a high ability for data fitting. Some distributional properties are derived for the general family. The Weibull distribution is then considered as the baseline, exhibiting a pliant four-parameter lifetime distribution. Five estimation methods for the related parameters are discussed. Bootstrap confidence intervals are also considered for these parameters. The distribution is reparametrized with location-scale parameters and it is used for a lifetime regression analysis. An extensive simulation is carried out on the estimation methods for distribution parameters and regression model parameters. Applications are given to two practical data sets to illustrate the applicability of the new family.

关键词: Marshall-Olkin family of distributions, Estimation, Confidence intervals, Bootstrap, Data analysis

Abstract: This paper introduces a new rich family of distributions based on mixtures and the so-called Marshall-Olkin family of distributions. It includes a wide variety of well-established mixture distributions, ensuring a high ability for data fitting. Some distributional properties are derived for the general family. The Weibull distribution is then considered as the baseline, exhibiting a pliant four-parameter lifetime distribution. Five estimation methods for the related parameters are discussed. Bootstrap confidence intervals are also considered for these parameters. The distribution is reparametrized with location-scale parameters and it is used for a lifetime regression analysis. An extensive simulation is carried out on the estimation methods for distribution parameters and regression model parameters. Applications are given to two practical data sets to illustrate the applicability of the new family.

Key words: Marshall-Olkin family of distributions, Estimation, Confidence intervals, Bootstrap, Data analysis

中图分类号:

Christophe Chesneau, Kadir Karakaya, Hassan S. Bakouch, Coşkun Kuş. An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1229-1257.

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An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications

An Alternative to the Marshall-Olkin Family of Distributions:Bootstrap, Regression and Applications

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