Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 1, 65-76

BEHAVIOUR OF SAMPLE COEFFICIENT OF VARIATION DRAWN FROM SEVERAL DISTRIBUTIONS

By

MURARI SINGH, International Crops Research Institute for the Semi-Arid Tropics and Virginia Polytechnic Institute and State University, Blacksburg

 

SUMMARY. Approximations to the first four moments of the inverse of sample coefficient of variation (ISCV) have been obtained using Fisher's K-statistics. A transformation for stabilizing the variance of ISCV has been considered. Three test statistics for testing the population coefficient of variation have been studied using their moment and distribution functions, and employed to obtain confidence interval for the inverse of the population coefficient of variation (IPCV). Eight distributions, namely, normal, logistic, Lapace, lognormal, chisquare, exponential, Weibull and Pareto distributions were taken for an evaluation of the various statistics. The approximations obtained for the bias and mean squared error of the ISCV appear adequate for most of the populations. Under several cases (of distributions and their parameters combinations), the statistics follow normal distributions and the confidence intervals based on these statistics provide adequate coverage probability for the IPCV. The statistics based on the inverse sinh transformation is suggested for its preference over the other statistics.

AMS(1980)subject classification. 62E15

Key words and phrases. Coefficient of variation, inverse in$h$ transformation, Fisher's $k$-statistics, non-normal population, normality, simulation

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This article in Mathematical Reviews.