Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Hasan, Sazib; Krishnamoorthy, K.

doi:10.2991/jsta.2017.16.3.6

Cited by 20 publications

(28 citation statements)

References 17 publications

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“…Table 1 records the 95% confidence interval for the ratio of the two coefficients of variation assuming that the data are obtained from independent lognormal distributions obtained by the methods discussed in this paper. Note that the MOVER method is identical to the Log method and Hasan and Krishnamoorthy [5] showed that results from the improved version of the MOVER method are still similar to those obtained by the Log method. Hence, both the MOVER method and its improved version are not included in the calculations.…”

Section: Real Data Examplementioning

confidence: 82%

“…Likelihood ratio Bartlett correction (5,5,5) 0.0658 0.0512 (5,10,15) 0.0646 0.0524 (10,10,10) 0.0565 0.0495 (10,15,20) 0.0529 0.0487 (50, 50, 50) 0.0544 0.0523…”

Section: Resultsunclassified

“…Ifṽar(loĝ), for = 1, 2, to be the same as that obtained in the Log method, the MOVER method is identical to the Log method. Note that Hasan and Krishamoorthy [5] proposed an improved version of the MOVER method.…”

Section: (4) Methods Of Variance Estimates Recovery (Mover)mentioning

confidence: 99%

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Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Jiang¹

2019

Journal of Probability and Statistics

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Without the ability to use research tools and procedures that yield consistent measurements, researchers would be unable to draw conclusions, formulate theories, or make claims about generalizability of their results. In statistics, the coefficient of variation is commonly used as the index of reliability of measurements. Thus, comparing coefficients of variation is of special interest. Moreover, the lognormal distribution has been frequently used for modeling data from many fields such as health and medical research. In this paper, we proposed a simulated Bartlett corrected likelihood ratio approach to obtain inference concerning the ratio of two coefficients of variation for lognormal distribution. Simulation studies show that the proposed method is extremely accurate even when the sample size is small.

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Section: Real Data Examplementioning

confidence: 82%

“…Likelihood ratio Bartlett correction (5,5,5) 0.0658 0.0512 (5,10,15) 0.0646 0.0524 (10,10,10) 0.0565 0.0495 (10,15,20) 0.0529 0.0487 (50, 50, 50) 0.0544 0.0523…”

Section: Resultsunclassified

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Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Jiang¹

2019

Journal of Probability and Statistics

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“…Simultaneous confidence intervals for the differences in the coefficients of variation of log-normal distributions were proposed by Thangjai, Niwitpong & Niwitpong (2016) and Thangjai, Niwitpong & Niwitpong (2020a). Moreover, Nam & Kwon (2017) and Hasan & Krishnamoorthy (2017) studied the confidence intervals for the ratio of coefficients of variation of two log-normal 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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“…Jafari and Kazemi [14] developed a parametric bootstrap (PB) approach. Some statisticians improved these tests for symmetric distributions [15][16][17][18][19][20][21][22][23]. The problem of comparing two or more CVs arises in many practical situations [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations

Zhang

Băleanu

2019

Symmetry

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Coefficient of variation (CV) is a simple but useful statistical tool to make comparisons about the independent populations in many research areas. In this study, firstly, we proposed the asymptotic distribution for the ratio of the CVs of two separate symmetric or asymmetric populations. Then, we derived the asymptotic confidence interval and test statistic for hypothesis testing about the ratio of the CVs of these populations. Finally, the performance of the introduced approach was studied through simulation study.

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Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Cited by 20 publications

References 17 publications

Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

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

Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations

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