Recursive relation for zero inflated Poisson mixture distributions

Abstract

The paper extends the work of Sarguta who derived recursive relations for univariate distributions by considering the ZIP continuous mixtures. The paper gives a recursive formular which can be used to evaluate the mixed distributions which can be used when the probability distribution functions cannot be evaluated explicitly. Integration by parts is often employed when deriving the recursive formulas. From section two up to section seven, we derived the recursive formulas for ZIP mixture distributions using Rectangular, Exponential, Gamma with two parameters, Poisson-Beta and Inverted-Beta as mixing distributions.