A study on the asymptotic distribution of maximum likelihood estimators for a two-parameter Weibul distribution in censored samples

Almir Mantovani[1]

Maria Aparecida de Paiva Franco[2]

§         ABSTRACT: The objective of this work is to study by simulation the asymptotic distribution of  maximum likelihood estimators of the parameters of a Weibull distribution, when observations are subject to random censorship. The study was made by supposing that C has a Uniform distribution in [0,c] and is independent of T. The inference is made from samples of (X,d), where X= min(T,C) and d is the indicator variable of the event (X=T). The study comprises the simulation of 1,000 samples of each one of the following sizes 10, 20 and 50. Several values of c giving different expected percentages of censored values in the sample were considered. The conclusion is that there is empirical evidence of an asymptotic normal distribution for each marginal distribution of the maximum likelihood estimators of parameters of Weibull distribution.

§       KEYWORDS: Survival analysis; censorship; maximum likelihood; simulation; Weibull.

[1]Departamento de Educação, Ciências Sociais e Política Internacional; Faculdade de História, Direito e Serviço Social; Universidade Estadual Paulista - UNESP, CEP14400-690, Franca, SP, Brasil. E-mail: almir@franca.unesp.br

[2]Departamento de Estatística, Universidade Federal de São Carlos - UFSCar, CEP 13565-905, São Carlos, SP, Brasil.