IMPROVED INFERENCE FOR THE SCALE PARAMETER IN THE LOMAX DISTRIBUTION BASED ON ADJUSTED PROFILE LIKELIHOOD FUNCTIONS

Abstract

In this thesis, we consider improving maximum likelihood inference for the scale parameter of the Lomax distribution. The improvement is based on using modification to the maximum likelihood estimator based on Barndorff-Nielsen's modified profile likelihood function. We apply this modification to obtain improved estimator for the scale parameter of the Lomax distribution in the presence of a nuisance shape parameter. Due to its complicated expressions, several approximations to Barndorff-Nielsen's modified profile log-likelihood function are used, including the modification based on the empirical covariances and the modification based on an ancillary statistic approximation. We consider complete as well as type I and type II censored data. Comparison between maximum profile likelihood estimator and modified profile likelihood estimators in terms of their biases and mean squared errors were carried out using simulation technique. We found that according to the criteria used, the point estimate of the Lomax scale parameter using the modified profile likelihood function based on empirical covariances approximation have the best performance under type I and type II censoring data. Examples based on real data are given to illustrate the methods considered in this thesis.