The Gamma-Weibull-G Family of Distributions with Applications

Broderick O. Oluyede, Shusen Pu, Boikanyo Makubate, Yuqi Qiu

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.
Original languageUndefined/Unknown
Pages (from-to)45-76
Number of pages32
JournalAustrian Journal of Statistics
Volume47
Issue number1
Publication statusPublished - Feb 1 2018

Cite this

Oluyede, Broderick O. ; Pu, Shusen ; Makubate, Boikanyo ; Qiu, Yuqi. / The Gamma-Weibull-G Family of Distributions with Applications. In: Austrian Journal of Statistics. 2018 ; Vol. 47, No. 1. pp. 45-76.
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The Gamma-Weibull-G Family of Distributions with Applications. / Oluyede, Broderick O.; Pu, Shusen; Makubate, Boikanyo; Qiu, Yuqi.

In: Austrian Journal of Statistics, Vol. 47, No. 1, 01.02.2018, p. 45-76.

Research output: Contribution to journalArticle

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AU - Pu, Shusen

AU - Makubate, Boikanyo

AU - Qiu, Yuqi

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AB - 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.

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