MVU estimation in a shifted gamma distribution

MVU estimation in a shifted gamma distribution with shape parameter a known integer

Muhammad El-Taha, Department of Mathematics and Statistics, University of Southern Maine

Abstract

In this paper a derivation of the minimum variance unbiased (MVU) point estimate for the scale parameter of a shifted (left-truncated) Gamma distribution will be given when the shape parameter, a, is a known integer. The explicit expression derived in this paper is of independent interest, and is computationally efficient for small a and small sample sizes; thus it may be considered complementary to the maximum likelihood method and its variants. Numerical comparisons show that, for small sample sizes, the MVU method outperforms the MLE method in most reported cases.