Confidence intervals for the median of a gamma distribution

Abstract

The gamma distribution is often used as a model for positively skewed distributions. The median is better than the mean as the representative of the 'average' in such situations. Literature is available for inference concerning the mean of a gamma distribution, but the literature concerning the median of a gamma distribution is rare.

In this paper we present a method for constructing confidence intervals for the median of a gamma distribution. The method involves inverting the likelihood ratio test to obtain 'large sample' confidence intervals. A difficulty arises as it is not possible to write the likelihood function in terms of the median. In this paper we propose a method to avoid this difficulty. The method works well even for moderately large sample sizes. The methodology is illustrated using an example.

Keywords and phrases: positively skewed, likelihood ratio test, large sample theory