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Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data.

North-West University, Potchefstroom Campus MSc (Mathematical Statistics), North-West University,Potchefstroom Campus 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. Masters

The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.

International audience; A new class of Bayesian estimators for a proportion in multistage binomial designs is considered. Priors belong to the beta-J distribution family, which is derived from the Fisher information associatedwith the design. The transposition of the beta parameters of theHaldane and the uniformpriors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs. We show that the estimator of the posterior mean based on the corrected Haldane prior and the estimator of the posterior mode based on the corrected uniform prior have good frequentist properties. An easy-to-use approximation of the estimator of the posteriormode is provided. The newBayesian estimators are compared to Whitehead's and the uniformly minimum variance estimators through several multistage designs. Last, the bias of the estimator of the posterior mode is derived for a particular case.