Document Type : Original Article

Authors

• Habiba Khatun ¹
• Manas Tripathy ²

¹ Department of MathematicsNational Institute of Technology RourkelaOdisha-769008India

² Department of Mathematics,National Institute of Technology RourkelaOdisha-769008India

Abstract

This article deals with the problems of testing the hypothesis on and interval estimation of the $p$-th quantile, $\xi = \mu+\eta \sigma_{1},$ where $\eta=-\log(1-p);$ $0<p<1$ of the first population, when samples are available from several exponential populations with a common location and possibly different scale parameters. 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. Several interval estimators for the quantile $\xi,$ such as confidence intervals based on generalized variable approach, parametric bootstrap approach and Bayesian intervals using Markov chain Monte Carlo (MCMC) method have been proposed. 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.

Keywords

• Average length
• Coverage probability
• Generalized variable method
• Computational approach test (CAT)
• Markov Chain Monte Carlo (MCMC) method
• Power and size of a test

Main Subjects

• Computational Statistics