Estimation for the scaled half logistic distribution under Type II censoring

We derive the best linear unbiased estimator (BLUE) based on doubly Type-II censored samples for the scaled half logistic distribution. Next, we derive the best linear unbiased estimator and the asymptotic best linear unbiased estimator based on k optimally selected order statistics and show that the asymptotic result provides very close approximation to the finite sample result even for a sample of size as small as 20. The maximum likelihood estimator (MLE) based on either complete or Type-II censored samples does not exist in explicit form. We determine its unbiasing factor and variance through Monte Carlo simulations employing a numerical iterative procedure. We derive an approximate maximum likelihood estimator (AMLE) which has an explicit form and is almost as efficient as the MLE and the BLUE. We illustrate all these methods of estimation with two examples.