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-WeibullG family of distributions (GWG). 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 R´enyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data
Highlights
Numerous classical distributions have been extensively discussed over the past years for modeling data in various areas such as economics, finance, insurance, actuarial, engineering, demography, biological studies, environmental and medical sciences
We introduce a new extended generator, the gamma-Weibull-G family based on their previous work and combined the gamma-generator with the Weibull-G family of distributions which was defined by (Bourguignon, Silva, and Cordeiro 2014)
The additional parameters induced by the Gamma-Weibull (G-W) generator induces a family of more flexible distributions
Summary
Numerous classical distributions have been extensively discussed over the past years for modeling data in various areas such as economics, finance, insurance, actuarial, engineering, demography, biological studies, environmental and medical sciences. Several methods for generating new families of distributions have been studied in recent years. Researchers often define new families of probability distributions that extend well-known distributions in order to provide great flexibility in modeling data in practice. (Alzaatreh and Ghosh 2014) introduced and studied the Weibull-X family of distributions, (Alzaatreh, Famoye, and Lee 2014) developed the properties of the gamma-X family of distributions in general and studied the gamma-normal distribution as a special case, and (Nascimento, Bourguignon, Zea, Santos-Neto, Silva, and Cordeiro 2014) introduced the gamma extended Weibull family of distributions. We introduce a new extended generator, the gamma-Weibull-G family based on their previous work and combined the gamma-generator with the Weibull-G family of distributions which was defined by (Bourguignon, Silva, and Cordeiro 2014).
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