Point and interval estimation for a generalized logistic distribution under progressive Type II censoring

The likelihood equations based on a progressively Type II censored sample from a Type I generalized logistic distribution do not provide explicit solutions for the location and scale parameters. We present a simple method of deriving explicit estimators by approximating the likelihood equations appropriately. We examine numerically the bias and variance of these estimators and show that these estimators are as efficient as the maximum likelihood estimators (MLEs). The probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are shown to be 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 the methods of inference developed here.