A Generalized Probability Distribution in Association With a Certain Generalized Hypergeometric Function

Yashwant Singh; Nanda Kulkarni

Volume : V, Issue : I, January - 2015

A Generalized Probability Distribution in Association With a Certain Generalized Hypergeometric Function

Yashwant Singh, Nanda Kulkarni

Abstract :

In this paper, a probability function has been introduced in terms of the –function and its properties are studied. It has shown that the classical non–central distributions such as, non–central chi–square, noncentral Student– , non–central and almost all classical central continuous distributions can be obtained as special cases of this general density function. This general density function is introduced with the hope that any density function, which can be represented in terms of any known special function as well as the density of the ratio of any two independent stochastic variables whose density functions can be represented in terms of any known special functions, is contained in as a special case. The various properties of , discussed in this paper, include the characteristic function, moments, recurrence relationship among moments and the distribution function.