The Gamma-Weibull-G Family of Distributions with Applications

Journal article

Authors / Editors

Makubate, Boikanyo

Research Areas

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Publication Details

Author list: Oluyede BO, Pu SS, Makubate B, Qiu YQ

Publisher: Austrian Society for Statistics

Place: WIEN

Publication year: 2018

Journal: Austrian Journal of Statistics (1026-597X)

Journal acronym: AUST J STAT

Volume number: 47

Issue number: 1

Start page: 45

End page: 76

Number of pages: 32

ISSN: 1026-597X

Languages: English-Great Britain (EN-GB)

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Abstract

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-Weibull-G (GWG) family of distributions. 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 Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data sets.

Keywords

Gamma distribution, Maximum likelihood estimation, Weibull-G distribution

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