Deriving Mixture Distributions Through Moment-Generating Functions

Abstract

This article aims to make use of moment-generating functions (mgfs) to derive the density of mixture distributions from hierarchical models. When the mgf of a mixture distribution doesn't exist, one can extend the approach to characteristic functions to derive the mixture density. This article uses a result given by E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80. The present work complements E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80 article with many new examples.