The Inverse Gamma Distribution and Some of Its Applications

Abstract

The inverse gamma distribution is of considerable theoretical and applied importance because of its distinctive positive support, right-skewed form, and capacity to model quantities for which large values are possible but increasingly unlikely.  It arises naturally in a variety of contexts, including Bayesian statistics, reliability theory, stochastic modeling, finance, and the analysis of variance and scale parameters.  Despite these applications and its historical significance within the Pearson system, the inverse gamma distribution receives comparatively limited attention in most – if not all - introductory probability and statistics curricula. The purpose of this paper is therefore twofold: first, to examine the historical development, mathematical properties, and applications of the inverse gamma distribution within the Pearson system; and second, to argue for its inclusion as a useful and pedagogically significant distribution in an undergraduate curriculum.