EXACT SAMPLING DISTRIBUTION OF SAMPLE COEFFICIENT OF VARIATION
Keywords:
Sample Coefficient of Variation, Sampling Distribution, Standard Normal Variate, Chi-Square Variate , Hyper-Geometric Distribution, Moments.Abstract
This paper proposes the sampling distribution of sample coefficient of variation from the normal population. We have derived the relationship between the sample coefficient of variation, standard normal and chi-square variate. We have derived density function of the sample coefficient of variation in terms of the confluent hyper-geometric distribution. Moreover, the first two moments of the distribution are derived and we have proved that the sample coefficient of variation (cv) is the biased estimator of the population coefficient of variation (CV). Moreover, the shape of the density function of sample co-efficient of variation is also visualized and the critical points of sample (cv) at 5% and 1% level of significance for different sample sizes have also been computed.
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