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A Unique Property of the Normal Distribution Associated with Perturbing a General Random Variable

Robin Willink
The American Statistician
Vol. 62, No. 2 (May, 2008), pp. 144-146
Stable URL: http://www.jstor.org/stable/27643994
Page Count: 3
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A Unique Property of the Normal Distribution Associated with Perturbing a General Random Variable
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Abstract

This article shows that when an independent perturbation is added to any nonnormal variable with finite moments the resulting variable is closer to normal when measured by each nonzero cumulant ratio. We also show that the normal density function is the only form of only of density with this property. This result provides weak evidence that the mixing of subpopulations of subjects can promote normality in the overall population.

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