Noninformative priors for the common shape parameter of several inverse Gaussian distributions

Abstract

Abstract In this paper, we develop the noninformative priors for the common shape parameterof several inverse Gaussian distributions. Specially, we want to develop noninformativepriors which satisfy certain objective criterion. The probability matching priors andreference priors of the common shape parameter will be developed. It turns out thatthe second order matching prior does not exist. The reference priors satisfy the rstorder matching criterion, but Je rey’s prior is not the rst order matching prior. Weshowed that the proposed reference prior matches the target coverage probabilities in afrequentist sense through simulation study, and an example based on real data is given.Keywords: Inverse Gaussian distribution, matching prior, reference prior, shape param-eter. 1. Introduction The probability density function (pdf) of inverse gaussian with parameters and isgiven byf(x) =r2ˇx 3 2 expˆ(x ) 2 2 2 x˙;x>0; (1.1)where >0 is mean parameter and >0 is the scale parameter. The shape parameter forthe inverse Gaussian distribution is de ned as , where = =. Because of the versatilityand exibility in modelling right-skewed data, the inverse gaussian distribution has poten-tially useful applications in a wide variety of elds such as biology, economics, reliabilitytheory and life testing as discussed in Chhikara and Folks (1989) and Seshadri (1999).The present paper focuses on noninformative priors for the common shape parameter ofseveral inverse Gaussian distributions. The shape parameter of inverse Gaussian distributionhas an important meaning. For example, Chhikara and Folks (1989) derived an exact methodof seeking a con dence interval for the ratio of means when the shape parameters of these