A unified form of gamma-type distributions

摘要

We study a mathematical model for a new distribution involving the generalized gamma function of Al-Musallam and Kalla (Further results on a generalized gamma function occurring in diffraction theory, Integral Transform. Spec. Funct. 7 (1998) 175–190). The probability density function (p.d.f.) is defined and some special cases are noted. We derive some basic functions associated with the p.d.f., namely, the mean, moment generating function, hazard rate function and mean residue life function. Comparative graphs of p.d.f., hazard rate function and mean residue life function are given. These graphs are found to reflect the role of shape and scale parameters.