Some Estimation Methods for Right Censored Data of Type II Related to Gumbel Distribution

Abstract

In this paper, right censored data of type II related to the Gumbel distribution (maximum extreme value distribution) of two parameters is considered. Estimation of the distribution parameters are presented by two methods: maximum likelihood method and modified moment method. Moments properties of the estimators such as bias, variance, skewness and kurtosis are compared between two methods. We show that the estimators are unbiased, and its variances converge to zero, which the estimators are consistent in modified moment method. Consistency of the maximum likelihood and modified moment estimators are tabulated by using mean square error. Confidence interval estimation for the distribution parameters based on the maximum likelihood method and modified moment method are given by Monte Carlo simulation.