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We develop noninformative priors for a ratio of parameters of two Maxwell distri-butions which is used to check the equality of two Maxwell distributions. Specially,we focus on developing probability matching priors and Je reys’ prior for objectiveBayesian inferences. The probability matching priors, under which the probability ofthe Bayesian credible interval matches the frequentist probability asymptotically, aredeveloped. The posterior propriety under the developed priors will be shown. Somesimulations are performed for identifying the usefulness of proposed priors in objectiveBayesian inference.Keywords: Matching prior, Maxwell distribution, ratio of parameters, reference prior. 1. Introduction Maxwell distribution is useful to study the relationship between the velocity of particle,temperature and mass. This distribution can be applied in the area of reliability, becausethe support of the distribution is non-negative. The statistical usage of Maxwell distributionwas investigated by Breitenberger (1963) and Bingham and Mardia (1978).In reliability area, Bekkera and Rouxa (2005) proposed maximum likelihood estimator,Bayes estimator and empirical Bayes estimator of reliability function. Their proposed esti-mators were compared through simulation study. Krishna and Malik (2009) compared Bayesestimator and maximum likelihood estimator of reliability function through simulation study.We propose statistical inference for the ratio of two parameters of Maxwell distributions.There can be found a little study for this issue in statistical literature. The ratio of parameterhas a meaning when one want to check the equality of two Maxwell distributions. Kang etal. (2012b) proposed likelihood based inference for the ratio of parameters. They developedsigned log-likelihood and modi ed signed log-likelihood statistics for testing the ratio.

Noninformative priors for the ratio of parameters of two Maxwell distributions