Maximum Likelihood Estimation for Two-Parameter Decreasing Hazard Rate Distributions Using Censored Data

Abstract

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard rate is estimated as a limiting case. Some computational methods are given and applications made.