UMVU Estimation in Gamma Model with Inliers at Zero and One

Inliers (instantaneous or early failures) are natural occurrences of a life test, where some of the items fail immediately or within a short time of the life test. These failures are either due to mechanical failures, accelerated pressures and interventions, or faulty items. The inconsistency of such life data is modeled using a nonstandard mixture of distributions; as there can be degeneracy in the model with discrete and continuous measures. The model discussed here is a nonstandard mixture of Gamma distribution with degeneracy happens at two discrete points at zero and one. In this paper, we provide the Uniformly Minimum Variance Unbiased (UMVU) estimation of parameters from a Gamma distribution with inliers at zero and one. Along with various other characteristics, the model was numerically illustrated on a real life example.