Maximum Likelihood Estimation for the Log-gamma Distribution under Type-II Censored Samples and Associated Inference

In this paper, we study the bias and variances of the maximum likelihood estimators (MLEs) of the location and scale parameters of the log-gamma distribution under Type II censored samples. We also derive the expected Fisher information matrix through which the asymptotic variances and covariance of the MLEs are tabulated for various proportions of censoring. The small-sample distributions of two pivotal quantities (useful for making inference for the location and scale paramters) are simulated by Monte Carlo method and the large-sample normal approximation is also described. Finally, a life-test data due to [27], and also analysed by [25], [26], is used to illustrate the method of estimation and inference developed in this paper.