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

doi:10.1007/s42967-021-00167-w

Abstract

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

CLC Number:

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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