Simultaneous Confidence Intervals for All Differences of Means of Normal Distributions with Unknown Coefficients of Variation

The delta-lognormal distribution is a combination of binomial and lognormal distributions, and so rainfall series that include zero and positive values conform to this distribution. The coefficient of variation is a good tool for measuring the dispersion of rainfall. Statistical estimation can be used not only to illustrate the dispersion of rainfall but also to describe the differences between rainfall dispersions from several areas simultaneously. Therefore, the purpose of this study is to construct simultaneous confidence intervals for all pairwise differences between the coefficients of variation of delta-lognormal distributions using three methods: fiducial generalized confidence interval, Bayesian, and the method of variance estimates recovery. Their performances were gauged by measuring their coverage probabilities together with their expected lengths via Monte Carlo simulation. The results indicate that the Bayesian credible interval using the Jeffreys’ rule prior outperformed the others in virtually all cases. Rainfall series from five regions in Thailand were used to demonstrate the efficacies of the proposed methods.

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Bayesian Confidence Intervals for Coefficients of Variation of PM10 Dispersion

Emerging Science Journal ◽

10.28991/esj-2021-01264 ◽

2021 ◽

Vol 5 (2) ◽

pp. 139-154

Author(s):

Warisa Thangjai ◽

Sa-Aat Niwitpong ◽

Suparat Niwitpong

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Confidence Intervals ◽

Bayesian Approach ◽

Normal Distributions ◽

Coefficients Of Variation ◽

The Difference ◽

Log Normal ◽

Log Normal Distribution ◽

The Bayesian Approach

Herein, we propose the Bayesian approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. For the first case, the Bayesian approach was compared with large-sample, Chi-squared, and approximate fiducial approaches via Monte Carlo simulation. For the second case, the Bayesian approach was compared with the method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using Monte Carlo simulation. The results show that the Bayesian approach provided the best approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. To illustrate the performances of the confidence limit construction approaches with real data, they were applied to analyze real PM10 datasets from the Nan and Chiang Mai provinces in Thailand, the results of which are in agreement with the simulation results. Doi: 10.28991/esj-2021-01264 Full Text: PDF

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A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

Sains Malaysiana ◽

10.17576/jsm-2021-5001-25 ◽

2021 ◽

Vol 50 (1) ◽

pp. 261-278

Author(s):

Warisa Thangjai ◽

Sa-Aat Niwitpong ◽

Suparat Niwitpong

Keyword(s):

Confidence Interval ◽

Normal Distribution ◽

Confidence Intervals ◽

Coefficient Of Variation ◽

Bayesian Approaches ◽

Normal Distributions ◽

Generalized Confidence Interval ◽

Coefficients Of Variation ◽

The Difference ◽

Highest Posterior Density

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

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