One Sample Empirical Likelihood Ratio Test for Coefficient of Variation
Keywords:
Chi-square approximation, simulation, Wald test, bootstrap test, type 1 error rate, power of the test, confidence intervalAbstract
Coefficient of Variation (CV) is widely used as a measure of variation by researchers in applied disciplines like chemistry, engineering, climatology, finance, agriculture and biological sciences. CV is a better measure for analysing health science data as the units of measurement of the index of different organs are often different. To assess precision in immunoassays and morphological measurements, CV is used. The present study aims to propose an empirical likelihood ratio (ELR) test for testing CV. The asymptotic null distribution of the proposed test statistic is obtained as Chi-square distribution with 1 degree of freedom. Simulation is carried out to check the adequacy of Chi-square approximation for finite samples. The proposed test is compared to Wald, bootstrap tests and ELR test constructed by Wang et al. (ELRT2) using real data sets and also simulated data sets. The study indicates that the proposed empirical likelihood ratio test possesses higher power compared to Wald, bootstrap and ELRT2 tests when the underlying distributions considered are normal, lognormal, gamma and Weibull
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