Unified probability density function involving a confluent hypergeometric function of two variables

摘要

In this paper first we define a new gamma-type function by means of an integral involving the confluent hypergeometric function of two variables Φ1(a,b,c;w,z). The gamma-type function is expressed in explicit form, using generalized hypergeometric series. Associated incomplete functions are defined, some special cases are noted and some relations for the new gamma-type function are given. A generalized probability density is considered, using the gamma-type function. This density represents a unified form for several gamma-type and inverse gaussian densities. A new probability density function with Gauss hypergeometric function is obtained. A number of known probability density functions follow as special cases. Some statistical functions, associated with the new density are obtained. Some figures are drawn for the probability density, to show the effect of the parameters involved. Results given recently by Al-Zamel, Ali et al. and others can be recovered from the formulas established here.