Distribution of the ratio of gamma variates

Abstract

The distribution of the ratio of independent gamma variates x and y each with shape parameters unity is studied, the ratio being t=x/(x+y). The problem arises from a model of ionic current fluctuations in biological membranes. Moments of the distribution are found, and an algorithm relating the fundamental parameter to the mean. This is used to set up percentage points. The moment estimator of the fundamental ratio parameter is defined as a series using Faà di Bruno's formulas for derivatives of a composite function (function of a function). Terms to order four in the sample size are given for mean and variance and compared to assessment using Pearson-Tukey transformations.

Keywords:

• Algorithm
• Faà di Bruno
• gamma distribution
• inverse series
• monotonicity
• percentage points
• ratio of gamma variates
• simulation