This article examines confidence intervals for the single coefficient of variation and the difference of coefficients of variation in the two-parameter exponential distributions, using the method of variance of estimates recovery (MOVER), the generalized confidence interval (GCI), and the asymptotic confidence interval (ACI). In simulation, the results indicate that coverage probabilities of the GCI maintain the nominal level in general. The MOVER performs well in terms of coverage probability when data only consist of positive values, but it has wider expected length. The coverage probabilities of the ACI satisfy the target for large sample sizes. We also illustrate our confidence intervals using a real-world example in the area of medical science.

Natural rainfall is necessary for agriculture in Thailand. Often, rainfall data contain zero and positive right-skewed observations. Within a given region, the mean rainfall can be used to evaluate how rainfall has changed over a period of time, and so, in this article, we propose interval estimates and an adjustment process based on the Bayesian approach to compute the rainfall amount mean. This includes highest posterior density intervals (HPDs) based on the beta (HPD-B), normal inverse chi-squared (HPD-NIC) and uniform (HPD-U) priors, which were compared with the existing methods. Coverage probability and relative average length were used to assess the performance of the methods by comparing their computation. A numerical evaluation showed that for a single mean and even chance of having zero observations, HPD-beta achieved the given target with small to moderate sample sizes, while HPD-U tended to perform very well with large sample size. To compare the difference between two means, HPD-U demonstrated excellent performance in almost all cases. Daily rainfall data from provinces in northern Thailand were used to confirm the efficacy of the new methods.

Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys’, the Jeffreys’ Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys’ prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.