Maximum Likelihood Estimation of the Parameters of the Weibull Distribution by Modified Quasilinearization

Abstract

An iterative procedure is given for joint maximum likelihood estimation of the three parameters of the Weibull population. For this population, the likelihood function is forned and the maximum likelihood equations are obtained. Simultaneous solution of these equations yields joint maximum likelihood estimators for the three parameters. The proposed iterative procedure is a modified quasilinearization algorithm for solving nonlinear equations with bounded variables. Numerical results are given in which the parameters are estimated from real and from simulated life test data drawn from the Weibull population.