The coefficient of variation (CV) is a widely used scaleless measure of variability in many disciplines. However the inference for the CV is limited to parametric methods or standard bootstrap. In this paper we propose two nonparametric methods aiming to construct confidence intervals for the coefficient of variation. The first one is to apply the empirical likelihood after transforming the original data. The second one is a modified jackknife empirical likelihood method. We also propose bootstrap procedures for calibrating the test statistics. Results from our simulation studies suggest that the proposed methods, particularly the empirical likelihood method with bootstrap calibration, are comparable to existing methods for normal data and yield better coverage probabilities for nonnormal data. We illustrate our methods by applying them to two real-life datasets.
Panichkitkosolkul W. Confidence intervals for the coefficient of variation in a normal distribution with a known population mean. Probab Stat J. 2013;Article ID 324940. DOI: 10.1155/2013/324940.)| false
Albatineh AN, Boubakari I, Kibria BMG. New confidence interval estimator of the signal-to-noise ratio based on asymptotic sampling distribution. Commun Stat Theory Meth. 2015. DOI: 10.1080/03610926.2014.1000498.)| false
Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics. 1963;5:375–383.
Gail MH, Gastwirth JL. A scale-free goodness-of-fit test for the exponential distribution based on the Gini statistic. J R Stat Soc Ser B. 1978;40:350–357.
Eisenberg DT. Telomere length measurement validity: the coefficient of variation is invalid and cannot be used to compare quantitative polymerase chain reaction and Southern blot telomere length measurement techniques. Int J Epidemiol. 2016;45:1295–1298.
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