Inference for the ratio of two exponential parameters using a Bayesian approach

Abstract

In this dissertation the maximal data information prior and the probability matching prior for the ratio of two exponential parameters will be derived. The method by Datta and Ghosh (1995) will be used to derive the probability matching prior and the method proposed by Zellner (1971) will be used to derive the maximal data information prior. Simulation studies will be done to compare and evaluate the performance of the following five priors: the Jeffreys, uniform, probability matching, maximal data information priors and a prior suggested by Ghosh et al. (2011). We will investigate the performance of the credibility intervals for the ratio of two exponential parameters. These intervals will be compared with each other in terms of coverage rates and average interval lengths. It seems that if inference is made on the ratio of two exponential parameters, the Jeffreys prior performs better in terms of coverage rates, but the maximal data information prior performs better in terms of average interval lengths. Loss functions will also be used to derive Bayes estimates. The squared error loss and all-or-nothing loss functions will be compared with each other through a simulation study. The performance of each loss function will be compared by looking at the MSE and bias values of the Bayes estimates. It seems that the Jeffreys prior with the absolute error loss performs better than the other considered priors and loss functions, when Bayesian point estimates of the ratio of two exponential parameters is computed. An application is also considered where the different credibility intervals and Bayes estimates are calculated and compared.