The extended gamma distribution with regression model and applications

Abstract

<abstract> <p>This paper introduces a new extension of the gamma distribution, named as a <italic>new extended gamma</italic> distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model.</p> </abstract>

On Modifications of the Gamma Function by Using Mittag-Leffler Function

“…Moreover, gamma distribution and its generalizations are of interest for a large audience (see [51] and the cited bibliography therein). Let us consider the following new probability density function of a statistical distribution for a random variable X as follows:…”

Beta Chi-Square Distributions Properties and Applications

“…These data have been analyzed by Feigl and Zelen (1965). The data set was recently studied by Woll et al (2014) and Altun et al (2021). Obtaining the maximum likelihood estimates (MLEs) for the distribution parameters, the maxLik function in maxLik-package of the statistical software R was used, and the iteration method was Newton Raphson.…”

A Flexible Extension to an Extreme Distribution

“…All of this has encouraged authors to work more on developing new lifetime distributions using different generalization methods. Here, we refer to the papers of [10] for the Marshall-Olkin class, [11] for the Beta and Gamma classes, [12] for the odd exponentiated half-logistic-G (OEHL-G) family, [13] for the flexible Weibull class, [14] for the odd log-logistic Lindley class, [15] for the odd Chen class, [16] for the exponentiated odd Chen class, [17] for a new Kumaraswamy generalized class, [18,19] for the extended Gamma and log-Bilal models, respectively, [20] for type I half logistic odd Weibull-G and [21] for the Poisson transmuted-G family, among others. Here, we use the OEHL-G family of distributions to build a new flexible model with three parameters.…”