Statistics of a Whiteness Measure
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A whiteness measure of a random number generator is defined as the sum of squares of all the off-zero elements of the sample covariance function of a finite segment of data of length K. The mean and variance of this whiteness measure are evaluated exactly, while its cumulative and exceedance distribution functions are determined by simulations. It is found that the variance of the whiteness measure must be broken into the two separate cases where K is even versus K is odd. This necessitates the analytic evaluation of some high-order moments in order to determine the variance exactly.... Statistics, Whiteness, Random numbers, Sample covariance, Mean, Variance.
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