Confidence Intervals for the Ratio of Coefficients of Variation in the Two-Parameter Exponential Distributions

Sangnawakij, Patarawan; Niwitpong, Sa-Aat; Niwitpong, Suparat

doi:10.1007/978-3-319-49046-5_46

Cited by 7 publications

(2 citation statements)

References 19 publications

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“…Niwitpong and WongKhao [30] provided estimators for the confidence bounds for the ratio of the CVs of normal distributions with known ratio of variances based on GVA and MOVER. Moreover, estimating the confidence interval for the ratio of the CVs of two two-parameter exponential distributions was achieved using MOVER and the generalized confidence interval (GCI) method by Sangnawakij et al [31]. Hasan and Krishnamoorthy [32] improved the confidence interval estimation for the ratio of the CVs of two lognormal distributions based on MOVER and the fiducial approach.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data

La-ongkaew

Niwitpong

2022

Symmetry

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The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where a process of transformation allows them to become symmetric. The Weibull distribution is commonly used to study the failure of components and phenomena. It has been applied to a variety of scenarios, including failure time, claims amount, unemployment duration, survival time, and especially wind speed data. A suitable area for installing a wind turbine requires a wind speed that is both sufficiently high and consistent, and so comparing the variation in wind speed in two areas is eminently desirable. In this paper, methods to estimate the confidence interval for the ratio of the coefficients of variation of two Weibull distributions are proposed and applied to compare the variation in wind speed in two areas. The methods are the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER), and Bayesian methods based on the gamma and uniform priors. The Bayesian methods comprise the equal-tailed confidence interval and the highest posterior density (HPD) interval. The effectiveness of the methods was evaluated in terms of their coverage probabilities and expected lengths and also empirically applied to wind speed datasets from two different areas in Thailand. The results indicate that the HPD interval based on the uniform prior outperformed the others in most of the scenarios tested and so it is suggested for estimating the confidence interval for the ratio of the coefficients of variation of two Weibull distributions.

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Section: Introductionmentioning

confidence: 99%

Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data

La-ongkaew

Niwitpong

2022

Symmetry

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“… Fung & Tsang (1998) compared parametric and nonparametric tests and Gokpinar & Gokpinar (2015) proposed a computational approach to test the equality of the coefficients of variation of k normal populations. Sangnawakij, Niwitpong & Niwitpong (2016) proposed two new confidence intervals for the ratio of the coefficients of variation of two-parameter exponential distributions. Sangnawakij & Niwitpong (2016) presented confidence interval estimation for the single coefficient of variation and the difference between two coefficients of variation in two-parameter exponential distributions.…”

Section: Introductionmentioning

confidence: 99%

Confidence intervals for the common coefficient of variation of rainfall in Thailand

Thangjai

Niwitpong

2020

PeerJ

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The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

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Confidence Intervals for Mean of Delta Two-Parameter Exponential Distribution

Khooriphan

Niwitpong

2022

Lecture Notes in Computer Science

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Confidence Intervals for the Ratio of Coefficients of Variation in the Two-Parameter Exponential Distributions

Cited by 7 publications

References 19 publications

Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data

Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data

Confidence intervals for the common coefficient of variation of rainfall in Thailand

Confidence Intervals for Mean of Delta Two-Parameter Exponential Distribution

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