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

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10004
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Daily Rainfall ◽  
Moisture Index ◽  
Interval Estimates ◽  
The Common ◽  
Log Normal ◽  
Confidence Interval Estimates

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.

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 &lt; 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.

Corrected Standard Errors with Clustered Data

2019 ◽  
Vol 28 (3) ◽  
pp. 318-339
Author(s):  
John E. Jackson
Keyword(s):  
Confidence Intervals ◽  
Standard Errors ◽  
Number Of Clusters ◽  
Interval Estimates ◽  
Explanatory Variables ◽  
Multiple Observations ◽  
Cluster Variation ◽  
Confidence Interval Estimates ◽  
Considerable Discussion ◽  
Robust Standard Errors

The use of cluster robust standard errors (CRSE) is common as data are often collected from units, such as cities, states or countries, with multiple observations per unit. There is considerable discussion of how best to estimate standard errors and confidence intervals when using CRSE (Harden 2011; Imbens and Kolesár 2016; MacKinnon and Webb 2017; Esarey and Menger 2019). Extensive simulations in this literature and here show that CRSE seriously underestimate coefficient standard errors and their associated confidence intervals, particularly with a small number of clusters and when there is little within cluster variation in the explanatory variables. These same simulations show that a method developed here provides more reliable estimates of coefficient standard errors. They underestimate confidence intervals for tests of individual and sets of coefficients in extreme conditions, but by far less than do CRSE. Simulations also show that this method produces more accurate standard error and confidence interval estimates than bootstrapping, which is often recommended as an alternative to CRSE.

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