In this paper, we will give a new application for the conditional inference for constructing the conditional confidence intervals for a shape-scale family parameters based on the generalized order statistics. For measuring the performances of this approach comparing to the unconditional inference, the covering percentage and their standard errors and the average lengths of the intervals have been obtained for different values of sample sizes and shape parameter, via Monte Carlo simulations. The simulation results indicated that the conditional intervals possess good statistical properties and they can perform quite well even when the sample size is extremely small comparing to the classical intervals based on the asymptotic maximum likelihood estimates (AMLEs). Finally, a numerical example is given to illustrate the confidence intervals developed in this paper.

Weibull distribution, Weibull extension model, modified Weibull model, Burr type XII distribution, Lamox distribution, generalized Pareto model, progressive type-II censored samples with binomial random removals, asymptotic maximum likelihood estimates.