Unbiased estimates of reliability for the truncated gamma distribution

This paper derives the minimum variance unbiased estimate of the reliability function associated with the gamma distribution which is right truncated at a known point by using the classical minimum variance unbiased estimation method as outlined and initiated by Basu (1964). The techniques given are general and can be used to estimate not only the probability in the upper tail (reliability) of a distribution but also the probability content of any other region. In the sequel, the distribution of the minimal sufficient statistic, useful in inferential problems, is also obtained. A result of Basu is deduced as a particular case.