Estimation of the location and scale parameters of the extreme value distmbution based on multiply type-II censored samples

Abstract

In this paper, we consider the problem of estimating the location and scale parameters of an extreme value distribution based on multiply Type-II censored samples. We first describe the best linear unbiased estimators and the maximum likelihood estimators of these parameters. After observing that the best linear unbiased estimators need the construction of some tables for its coefficients and that the maximum likelihood estimators do not exist in an explicit algebraic form and hence need to be found by numerical methods, we develop approximate maximum likelihood estimators by appropriately approximating the likelihood equations. In addition to being simple explicit estimators, these estimators turn out to be nearly as efficient as the best linear unbiased estimators and the maximum likelihood estimators. Next, we derive the asymptotic variances and covariance of these estimators in terms of the first two single moments and the product moments of order statistics from the standard extreme value distribution. Finally, we present an example in order to illustrate all the methods of estimation of parameters discussed in this paper.

Keywords:

• order statistics
• Type-II censored samples
• location and scale parameters
• extreme value distribution
• Weibull distribution
• best linear unbiased estimators
• maximum likelihood estimators
• approximate maximum likelihood estimators
• bias
• mean square error
• lifetime data