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A family of Gamma-generated distributions: Statistical properties and applications

Hormatollah Pourreza, , Einolah Deiri
Statistical Methods in Medical Research ; doi:10.1177/09622802211009262

Abstract: In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15
Keywords: Gamma-X distribution / hazard rate function / Gamma-Weibull distribution / incomplete Gamma function / maximum likelihood estimation / COVID-19

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