Inference for the Scaled Half-Logistic Distribution Based on Progressively Type-II Censored Samples

For the half-logistic distribution, the maximum likelihood method does not provide an explicit estimator for the scale parameter based on a progressively Type-II censored sample. In this article, we first present a simple method of deriving an explicit estimator by approximating the likelihood function. We then examine through simulations the bias and variance of this estimator and show that this estimator is as efficient as the maximum likelihood estimator (MLE). Next, we show that the probability coverages of the pivotal quantities (for the scale parameter) based on asymptotic normality are unsatisfactory, especially when the effective sample size is small. Therefore, we suggest using unconditional simulated percentage points of these pivotal quantities for the construction of confidence intervals. A wide range of sample sizes and progressive censoring schemes have been considered in this study. Finally, we present a numerical example to illustrate all the methods of inference discussed here.