McKay's approximation for the coefficient of variation
In statistics, McKay's approximation of the coefficient of variation is a statistic based on a sample from a normally distributed population. It was introduced in 1932 by A. T. McKay. Statistical methods for the coefficient of variation often utilizes McKay's approximation.
Let , be independent observations from a normal distribution. The population coefficient of variation is . Let and denote the sample mean and the sample standard deviation, respectively. Then is the sample coefficient of variation. McKay’s approximation is
Note that in this expression, the first factor includes the population coefficient of variation, which is usually unknown. When is smaller than 1/3, then is approximately chi-square distributed with degrees of freedom. In the original article by McKay, the expression for looks slightly different, since McKay defined with denominator instead of . McKay's approximation, , for the coefficient of variation is approximately chi-square distributed, but exactly noncentral beta distributed .
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- Iglevicz, Boris; Myers, Raymond (1970). "Comparisons of approximations to the percentage points of the sample coefficient of variation". Technometrics 12 (1): 166–169. JSTOR 1267363.
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- Forkman, Johannes. "Estimator and tests for common coefficients of variation in normal distributions". Communications in Statistics - Theory and Methods 38. pp. 21–26. Retrieved 2013-09-23.
- Forkman, Johannes; Verrill, Steve. "The distribution of McKay's approximation for the coefficient of variation". Statistics & Probability Letters 78. pp. 10–14. doi:10.1016/j.spl.2007.04.018. Retrieved 2013-09-23.