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

Abstract

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.

D. A. S. Fraser: From structural inference to asymptotics

“…Regression models are illustrated in Fraser, Wong & Wu (1999), Fraser, Rekkas & Wong (2005), and Fraser, Wong & Sun (2009); the latter paper considers the Box‐Cox transformed‐regression model as one of the examples. Don's PhD student Augustine Wong, with his collaborators and students, has published a wealth of examples; see, for example, Wong & Jiang (2019) and Qi, Rekkas & Wong (2018). Belzile & Davison (2022) apply the tangent exponential model to inference about extreme values and threshold exceedances.…”

Confidence intervals for rainfall dispersions using the ratio of two coefficients of variation of lognormal distributions with excess zeros

“…Hasan and Krishnamoorthy [ 21 ] suggested MOVER and the fiducial method to establish confidence intervals for small sample sizes from lognormal distributions. Wong and Jiang [ 22 ] proposed the Bartlett-corrected likelihood ratio method to construct confidence intervals for lognormal distributions. In addition, Sangnawakij and Niwitpong [ 23 ] used the score and Wald methods to construct confidence intervals for the CV and function of CVs with bounded parameter spaces in two gamma distributions for which both proposed methods were evidently suitable.…”

Improved Confidence Interval and Hypothesis Testing for the Ratio of the Coefficients of Variation of Two Uncorrelated Populations

“…They obtained the estimate using the Fieller-type log method of variance estimates recovery (MOVER) and the Wald-type method. Two other researchers, Jiang and Wong [26], used the Barlett's modified likelihood ratio simulation method to make inferences about the ratio of two CVs in the lognormal distribution.…”