In the present paper, a probability function has been introduced in terms of the -function and its properties are studied. It is shown that the classical non-central distributions such as, non-central chi-square, non-central 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

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... nown 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 properties of , discussed in this paper, include the characteristic function, moments, recurrence relationship among moments and the distribution function.