Some generalized distributions based on Stacy's generalized gamma distribution

Abstract

The generalized gamma distribution having the density function was introduced by Stacy (1962), who studied some of its properties. As observed by Stacy, many standard distributions are special cases of (1). For example d=p=1 gives the exponential, p=1 gives the gamma p=1 and d=n/2 (n is a positive integer) gives the chi-squared, and d=p gives the Weibull distribution. Furthermore, certain functions of a normal variable— viz., its positive even powers, its modulus, and all positive powers of its modulus, have Stacy's gamma form.