Parameter-rich unconditional distributions with a stochastic parameter in the conditional gamma distribution

Abstract

Suppose that the scale parameter in the two-parameter gamma distribution (as conditional distribution) is a function of a variate. This stochastic scale parameter is determined by the form which the regression curve can assume. Parameter-rich unconditional distributions with the two-parameter gamma distribution as a mixed distribution are derived for the regres­sion functions ay and a/y. A generalized distribution is used as a mixed distribution to derive a wide class of unconditional distributions with enrichment induced by regression parameters.