On Methods of Estimation for the Type II Discrete Weibull Distribution

In this paper, we describe and analyze several methods of estimation for the type II discrete Weibull distribution, outlining their applicability and properties, assessing and comparing their performance via intensive Monte Carlo simulation experiments. We consider the standard maximum likelihood method, a method of proportion, and two variants of the least-squares method. The type II discrete Weibull distribution can be used in reliability engineering for modeling count data or discrete lifetimes and its use is theoretically motivated by its capability of modeling either bounded or unbounded support, and either increasing or decreasing failure rate. Statistical analyses of real datasets are presented to show the capability of the distribution in fitting reliability data and illustrate the application of the proposed inferential techniques.