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In [[statistics]], '''McKay's approximation''' of the [[coefficient of variation]] is a statistic based on a sample from a [[normal distribution|normally distributed]] population. It was introduced in 1932 by A. T. McKay.<ref>McKay, A. T. (1932) Distribution of the coefficient of variation and the extended “t” distribution. ''Journal of the Royal Statistical Society'' 95, 695–698</ref> Statistical methods for the coefficient of variation often utilizes McKay's approximation.<ref>{{cite journal |jstor=1267363 |title=Comparisons of approximations to the percentage points of the sample coefficient of variation |year=1970 |last1=Iglevicz |first1=Boris |last2=Myers |first2=Raymond |journal=Technometrics |volume=12 |issue=1 |pages=166–169}}</ref><ref>Bennett, B. M. (1976). On an approximate test for homogeneity of coefficients of variation. In: Ziegler, W. J. (ed.) ''Contributions to Applied Statistics Dedicated to A. Linder. Experentia Suppl.'' 22, 169-171</ref><ref>{{cite journal |jstor=2685039 |title=Confidence intervals for a normal coefficient of variation |year=1996 |last1=Vangel |first1=Mark G. |journal=The American Statistician |volume=50 |issue=1 |pages=21–26}}.</ref><ref>{{cite web| url=http://pub.epsilon.slu.se/4489/1/forkman_j_110214.pdf | title=Estimator and tests for common coefficients of variation in normal distributions | accessdate=2013-09-23 |last1=Forkman |first1=Johannes |journal=Communications in Statistics - Theory and Methods |volume=38 |pages=21–26}}</ref>
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Let <math> x_i </math>, <math>i = 1, 2,\ldots, n</math> be <math> n </math> independent observations from a <math> N(\mu, \sigma^2) </math> normal distribution. The population coefficient of variation is <math> c_v = \sigma / \mu </math>. Let <math> \bar{x} </math> and <math> s \,</math> denote the [[sample mean]] and the [[sample standard deviation]], respectively. Then <math> \hat{c}_v = s/\bar{x} </math> is the sample coefficient of variation. McKay’s approximation is
:<math>
K = \left( 1 + \frac{1}{c_v^2} \right) \ \frac{(n - 1) \ \hat{c}_v^2}{1 + (n - 1) \ \hat{c}_v^2/n}
</math>
<!-- WHAT is \gamma?? -->
Note that in this expression, the first factor includes the population coefficient of variation, which is usually unknown. When <math> c_v </math> is smaller than 1/3, then <math> K </math> is approximately [[chi-squared distribution|chi-square distributed]] with <math> n - 1 </math> degrees of freedom. In the original article by McKay, the expression for <math> K </math> looks slightly different, since McKay defined <math> \sigma^2 </math> with denominator <math> n </math> instead of <math> n - 1 </math>. McKay's approximation, <math> K </math>, for the coefficient of variation is approximately chi-square distributed, but exactly [[noncentral beta distribution|noncentral beta distributed]]
.<ref>{{cite web| url=http://pub.epsilon.slu.se/3317/1/Forkman_Verrill_080610.pdf | title=The distribution of McKay's approximation for the coefficient of variation | accessdate=2013-09-23 |last1=Forkman |first1=Johannes |last2=Verrill |first2=Steve |journal=Statistics & Probability Letters |volume=78 |pages=10–14}}</ref>
 
== References==
<references/>
 
[[Category:Statistical deviation and dispersion]]

Latest revision as of 04:29, 15 February 2014

In exchange for guaranteed coverage, you will be charged a higher term life insurance premium. Nevertheless, its benefits are a lot more than term-life insurance policies. Such companies have to meet strict requirements concerning their suitability for such business. The body mass index is something the modern life insurance agents are very particular about. Variable life insurance Chico: This sort of life insurance Chico vehicle permits you to select how the revenue you place with in it is actually invested. Here are six factors that you need to look into whenever you are researching term life insurance ratings and insurance providers -. While I can certainly understand how the person feels; the reality, rather than the perception, is that this person actually can.

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