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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.

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.