The Relative Potency of Two Drugs Using the Confidence Interval for Ratio of Means of Two Normal Populations with Unknown Coefficients of Variation

2022 ◽  
Vol 11 (1) ◽  
pp. 1-14
Keyword(s):  
Confidence Interval ◽  
Relative Potency ◽  
Normal Populations ◽  
Coefficients Of Variation

Constructing a confidence interval for the ratio of normal distribution quantiles

2020 ◽  
Vol 26 (4) ◽  
pp. 325-334
Author(s):  
Ahad Malekzadeh ◽  
Seyed Mahdi Mahmoudi
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Pivotal Quantity ◽  
Simple Method ◽  
Normal Populations ◽  
Generalized Pivotal Quantity ◽  
Variance Estimate

AbstractIn this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

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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