Abstract

In this study, we define the chi-square  mixture of transformed gamma distribution which contained some special submodels namely, the chi-square  mixture of gamma, Weibull, and  exponential mixture distributions. Also, the chi-square  mixture of inverse transformed gamma distribution is defined and a class of submodels are deduced, that is, the chi-square  mixture of inverse  gamma, inverse Weibull, and inverse exponential mixture distributions. For both classes, statistical properties are investigated, that is, mean, variance, skewness and kurtosis using $r$th raw moment. The limiting behavior and   special cases are also given to established relationships.

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