Methods for Fitting the Right‐Truncated Weibull Distribution to Life‐Test and Survival Data

Abstract

AbstractThis paper develops mathematical and computational methods for fitting, by the method of maximum likelihood (ML), the two‐parameter, right‐truncated Weibull distribution (RTWD) to life‐test or survival data. Some important statistical properties of the RTWD are derived and ML estimating equations for the scale and shape parameters of the RTWD are developed. The ML equations are used to express the scale parameter as an analytic function of the shape parameter and to establish a computationally useful lower bound on the ML estimate of the shape parameter. This bound is a function only of the sample observations and the (known) truncation point T. The ML equations are reducible to a single nonlinear, transcendental equation in the shape parameter, and a computationally efficient algorithm is described for solving this equation. The practical use of the methods is illustrated in two numerical examples.