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Abstract In this paper, we develop the noninformative priors for the ratio of the scale parameters in the invertedexponential distributions. The rst and second order matching priors, the reference prior and Jereys prior aredeveloped. It turns out that the second order matching prior matches the alternative coverage probabilities, is acumulative distribution function matching prior and is a highest posterior density matching prior. In addition, thereferencepriorandJereys’priorarethesecondordermatchingprior. Weshowthattheproposedreferencepriormatches the target coverage probabilities in a frequentist sense through a simulation study as well as provide anexample based on real data is given.Keywords: Inverted exponential distribution, matching prior, reference prior, scale parameter. 1. Introduction Exponential distribution is the most exploited distribution for lifetime data analysis. However, itssuitabilityisrestrictedtoaconstanthazardrate,whichisdiculttojustifyinmanypracticalproblems.This leads to the development of alternative models for lifetime data. A number of distributions suchasWeibullandgammahavebeenextensivelyusedtoanalyzelifetimedatasuchassituationswherethehazard rate is monotonically increasing or decreasing; however, the non-monotonicity of the hazardrate has also been observed in many situations. For example, the hazard rate initially increases withtime and reaches a peak after some nite period of time and then declines slowly in some studies ofmortality associated with particular diseases. Thus, the need to analyze such data whose hazard rateis non-monotonic was realized and suitable models were proposed. Killer and Kamath (1982), Lin

Noninformative Priors for the Ratio of the Scale Parameters in the Inverted Exponential Distributions