Estimation of P(X<Y) for generalized half logistic distribution based on Type-II censored data

The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups.

This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration.

The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior.

The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.