Confidence Intervals for the Ratio of Coefficients of Variation of the Gamma Distributions

2015 ◽  
pp. 193-203 ◽  
Author(s):  
Patarawan Sangnawakij ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Gamma Distributions ◽  
Coefficients Of Variation

Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

2021 ◽  
Author(s):  
Theerapong Kaewprasert ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Bayesian Method ◽  
Simulation Studies ◽  
Jeffreys Prior ◽  
Inverse Gamma ◽  
Gamma Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
Percentile Bootstrap ◽  
Better Than

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

scholarly journals Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation

Mathematics ◽  
2017 ◽  
Vol 5 (3) ◽  
pp. 39 ◽  
Author(s):  
Warisa Thangjai ◽  
Suparat Niwitpong ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Normal Distributions ◽  
Coefficients Of Variation

Electronic Somatic Cell Count—Chemical Method, DMSCC, and WMT Tests for Raw Milk

1976 ◽  
Vol 39 (12) ◽  
pp. 854-858 ◽  
Author(s):  
D. R. THOMPSON ◽  
V. S. PACKARD ◽  
R. E. GINN
Keyword(s):  
Somatic Cell ◽  
Cell Count ◽  
Confidence Intervals ◽  
Somatic Cell Count ◽  
Raw Milk ◽  
Field Method ◽  
Regression Equations ◽  
Somatic Cell Counts ◽  
Cell Counts ◽  
Coefficients Of Variation

The Direct Miscroscopic Somatic Cell Count — field method (DMSCC), Wisconsin Mastitis Test (WMT), and Electronic Somatic Cell Count (ESCC) were studied to determine variability and relationship to each other. The coefficients of variation computed at a DMSCC count near one million were 15.6% (DMSCC), 6.3% (WMT), and 4.2% (ESCC). Linear regression equations were determined for predicting DMSCC results by WMT and ESCC. The approximate width of the 95% confidence intervals for ESCC predicting DMSCC were ± 275,000 and for WMT predicting DMSCC were ± 600,000. The prediction of square root and log transformations of DMSCC by WMT exhibited narrower confidence intervals for low somatic cell counts, but wider intervals for high counts (greater than 1,000,000).

Reliability of Pharmacodynamic Analysis by Logistic Regression

2000 ◽  
Vol 92 (4) ◽  
pp. 985-992 ◽  
Author(s):  
Wei Lu ◽  
James M. Bailey
Keyword(s):  
Logistic Regression ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Parameter Estimates ◽  
True Parameter ◽  
True Value ◽  
Coefficients Of Variation ◽  
Effect Relation ◽  
Log Normal ◽  
Multiple Patients

Background Many pharmacologic studies record data as binary yes-or-no variables, and analysis is performed using logistic regression. This study investigates the accuracy of estimation of the drug concentration associated with a 50% probability of drug effect (C50) and the term describing the steepness of the concentration-effect relation (gamma). Methods The authors developed a technique for simulating pharmacodynamic studies with binary yes-or-no responses. Simulations were conducted assuming either that each data point was derived from the same patient or that data were pooled from multiple patients in a population with log-normal distributions of C50 and gamma. Coefficients of variation were calculated. The authors also determined the percentage of simulations in which the 95% confidence intervals contained the true parameter value. Results The coefficient of variation of parameter estimates decreased with increasing n and gamma. The 95% confidence intervals for C50 estimation contained the true parameter value in more than 90% of the simulations. However, the 95% confidence intervals of gamma did not contain the true value in a substantial number of simulations of data from multiple patients. Conclusion The coefficient of variation of parameter estimates may be as large as 40-50% for small studies (n < or = 20). The 95% confidence intervals of C50 almost always contain the true value, underscoring the need for always reporting confidence intervals. However, when data from multiple patients is naively pooled, the estimates of gamma may be biased, and the 95% confidence intervals may not contain the true value.

scholarly journals The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

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.

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