Bayesian inference for the common location parameter of several shifted-exponential populations

Abstract

Consider k random samples which are independently drawn from k shifted-exponential distributions, with respective scale parameters σ 1 , σ 2 , … , σ k and common location parameter θ . On the basis of the given samples and in a Bayesian framework, we address the problem of point and interval estimation of the location parameter θ under the conjugate priors, which are usually proper priors. Moreover, we also address the problem of testing the equality of the location parameters. We propose Bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Our proposed Bayesian procedures are compared and contrasted, via a comparison study, a simulation study, and a real-world data analysis, to the existing classical exact procedures proposed by Tippett (Tippett’s method (Tippett, 1931)), Fisher (Fisher’s method (Fisher, 1932)), Stouffer (Inverse normal method (Stouffer et al., 1949)), and George (Logit method (George, 1977)), and to the generalized variable procedures proposed by Tsui and Weerahandi (Generalized p -value method (Tsui and Weerahandi, 1989)).