A Quasi-Normal Distribution and its Application in Parameter Estimation on Heavily Censored Data

Abstract

Parameter estimation on heavily censored data is a challenging issue. This paper addresses this issue using a two-step single-parameter maximum likelihood method to estimate mean time to failure (MTTF) and Weibull shape parameter (WSP). The first step fits the data to three one-parameter auxiliary models, which are special cases of a two-parameter quasi-normal distribution with nonnegative support, to obtain three estimates of the MTTF. The second step estimates the WSP through fixing each of the MTTF estimates. The best estimates are selected from three pairs of estimates based on appropriate rules. A simple numerical method is also proposed to construct the confidence intervals of the estimated MTTF and WSP. The auxiliary models are derived, the model selection rules are specified, and a numerical experiment is carried out to illustrate the accuracy of the proposed method.