Estimation of Parameters of a Three-Parameter Weibull Distribution Based on Censored Data

Abstract

In this thesis, parameters of a three-parameter Weibull distribution model are estimated based on a combination of both progressive and fixed type-I censoring using the techniques of maximum likelihood estimation, Corrected maximum likelihood estimation and Weighted maximum likelihood estimation. The objectives were to identify the best estimators for the three-parameter Weibull models’ parameters based on fixed type I and progressively censored subjects by investigating their properties as well as analyzing the effect of both sample size and shape parameter to the resulting parameter estimates. Different samples sizes (20, 40, 60, 80, and 100) were considered and simulated with 25% of each being censored. The 25% were divided into progressive and fixed type-I censoring scheme. Davidon-Fletcher-Powell (DFP) optimization method in MATLAB program was used in estimation of the parameters from the parametric models by iteration with a one-step bias-correction as initial estimates for the required iterative procedure. Application was made to the Internally Displaced Persons dataset. Discussion was made on the parameter estimates of the three-parameter Weibull distribution from the three techniques based on a mixture progressive and fixed Type-I right censored sample. Different estimation procedures are studied and compared through a Monte Carlo simulation study. Based on the simulation results, the weighted maximum likelihood estimates was found to be superior in estimating the parameters of the Weibull distribution in terms of its bias, total deviation and Root Mean Square Error.