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.
