Inference on Quantiles of Several Exponential Populations with a Common Location: Hypothesis Testing and Interval Estimation

This article deals with the problems of testing the hypothesis and interval estimation of the p-th quantile, ξ = μ+ησ1, where η=-log(1-p), (0<p<1) of the first population when samples are available from several exponential populations with a common location and possibly different scales. Several test procedures, such as tests using a generalized variable approach, tests based on parametric bootstrap method, and tests using a computational approach to test the null hypothesis against a suitable alternative, have been proposed. Besides several interval estimators for the quantile η, such as confidence intervals based on generalized variable approach, parametric bootstrap approach and Bayesian intervals using Markov chain Monte Carlo (MCMC) method have been suggested. The confidence intervals are compared through their coverage probabilities and average lengths, whereas the test statistics are compared in terms of powers and sizes numerically. The application of our model problem has been shown using real-life data sets, and conclusions have been made there.