Applying medical survival data to estimate the three-parameter Weibull distribution by the method of probability-weighted moments

The method of probability-weighted moments is used to derive estimators of parameters and quantiles of the three-parameter Weibull distribution. The p roperties of these estimators are studied. The results obtained are compare d with those obtained by using the method of maximum likelihood. The Weibul l probability distribution has numerous applications in various areas: for example, breaking strength, Life expectancy, survival analysis and animal b ioassay. Because of its useful applications, its parameters need to be eval uated precisely, accurately and efficiently. There is a rich literature ava ilable on its maximum likelihood estimation method. However, there is no ex plicit solution for the estimates of the parameters or the best linear unbi ased estimates. Further, the Weibull parameters cannot be expressed explici tly as a function of the conventional moments and iterative computational m ethods are needed. The maximum likelihood methodology is based on large-sam ple theory and the method might not work well when samples are small or mod erate in size. Others have proposed a class of moments called probability-w eighted moments. This class seems to be interesting as a method for estimat ing parameters and quantiles of distributions which can be written in inver se form. Such distributions include the Gumbel, Weibull, logistic, Tukey's symmetric lambda, Thomas Wakeby, and Mielke's kappa. It has been illustrate d that rather simple expressions for the parameters can be written in inver se form in terms of probability-weighted moments (PWMs) for most of these d istributions. In this paper we define the PWM estimators of the parameters for the three-parameter Weibull distribution. We investigate the properties of these estimators in a medical application setting. We also examine the added influence that censored data may have on the estimates. (C) 1999 IMAC S/Elsevier Science B.V. All rights reserved.