MODIFIED GAMMA DISTRIBUTION WITH SINGULARITY AT ZERO

Abstract

ABSTRACT There are many situations in life testing experiment where an item fails instantaneously and hence the observed lifetime is reported as zero. Similarly in the case of rainfall data, there may be days reported with zero rainfall corresponding to the dry days during the season. We propose a modified Gamma distribution as a suitable model to represent such situations by mixture of a singular distribution at zero and a two parameter Gamma distribution. We first show that this mixture model is a three-parameter exponential family and derive Maximum Likelihood Estimates of the parameters and their joint asymptotic distributions as well as that of the mean. Based on the above results a 95% confidence interval for the mean of the mixture distribution is obtained. The method is illustrated with actual measured data on rainfall from two stations namely, Jalgaon and Coimbatore in India.