The Gamma Power Half-Logistic Distribution: Theory and Applications
Résumé
In this paper, we propose a new three-parameter distribution on the positive real line, called the gamma power half-logistic distribution. This new distribution is derived to the gamma-G family of distributions pioneered by Zografos and Balakrishnan (2009) and the power half-logistic distribution introduced by Krishnarani (2016). Among its advantages, the corresponding hazard rate function has various kinds of shapes, which constitutes a positive point in the context of statistical modelling. A part of the paper is devoted to some of its main mathematical features, including quantiles, skewness, kurtosis, moments, incomplete moments, mean deviations, Bonferroni and Lorenz curves, stochastic ordering, reliability parameter and distribution of order statistics. Then, the gamma power half-logistic model is investigated in view of data analysis. We use the maximum likelihood method for estimating the model parameters, with a simulation study attesting the good performance of the method. The practical aspect is discussed with the help of two real life data sets.
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