The gamma log-logistic Weibull distribution: model, properties and application

Journal article

Authors / Editors

Makubate, Boikanyo

Research Areas

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Publication Details

Author list: Foya S, Oluyede BO, Fagbamigbe AF, Makubate B

Publisher: Universita del Salento

Place: LECCE

Publication year: 2017

Journal: Electronic Journal of Applied Statistical Analysis (2070-5948)

Journal acronym: ELECTRON J APPL STAT

Volume number: 10

Issue number: 1

Start page: 206

End page: 241

Number of pages: 36

ISSN: 2070-5948

eISSN: 2070-5948

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, a new generalized distribution called the gamma log-logistic Weibull (GLLoGW) distribution is proposed and studied. The GLLoGW distribution include the gamma log-logistic, gamma log-logistic Rayleigh, gamma log logistic exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic as well as other special cases as sub models. Some mathematical properties of the new distribution including moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Renyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A Monte Carlo simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and an application to real dataset to illustrate the usefulness of the model is given.

Keywords

Gamma distribution, Log-logistic Weibull distribution, Maximum likelihood estimation, Weibull distribution

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