The Odd Gamma Weibull-Geometric Model: Theory and Applications

Rana Muhammad Imran Arshad, Christophe Chesneau and Farrukh Jamal
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Rana Muhammad Imran Arshad: Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
Christophe Chesneau: Department of Mathematics, LMNO, University of Caen, 14032 Caen, France
Farrukh Jamal: Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan

Mathematics, 2019, vol. 7, issue 5, 1-18

Abstract: In this paper, we study a new four-parameter distribution called the odd gamma Weibull-geometric distribution. Having the qualities suggested by its name, the new distribution is a special member of the odd-gamma-G family of distributions, defined with the Weibull-geometric distribution as baseline, benefiting of their respective merits. Firstly, we present a comprehensive account of its mathematical properties, including shapes, asymptotes, quantile function, quantile density function, skewness, kurtosis, moments, moment generating function and stochastic ordering. Then, we focus our attention on the statistical inference of the corresponding model. The maximum likelihood estimation method is used to estimate the model parameters. The performance of this method is assessed by a Monte Carlo simulation study. An empirical illustration of the new distribution is presented by the analyses two real-life data sets. The results of the proposed model reveal to be better as compared to those of the useful beta-Weibull, gamma-Weibull and Weibull-geometric models.

Keywords: Weibull distribution; gamma distribution; hazard rate function; lifetime data; maximum likelihood method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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