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Moments of a statistic caused by random combinations or random matings

Authors:	Shinji Azuma Kenji Hayashi Akio Kudô

Institution:	(1) Science University of Tokyo, Tokyo, Japan;(2) Kyushu University, Kyushu, Japan

Abstract:	Summary Given two sets of sizek, {α ₁...,α _k} and {β ₁...,β _k} there arek! possible combinations of these two $\left\{ {\left( {\alpha _1 ,\beta _{l_1 } } \right), \cdots ,\left( {\alpha _k ,\beta _{l_k } } \right)} \right\}$ , and suppose there is apriori given a number corresponding to the partnership (α ₁,β _j}. The average of the numbers corresponding to $\left\{ {\left( {\alpha _1 ,\beta _{l_1 } } \right), \cdots ,\left( {\alpha _k ,\beta _{l_k } } \right)} \right\}$ is a random variable, and this paper presents the first five moments of the average, and an application in the study of an isolated human population is demonstrated.

Keywords:	Random combination Gram-Chalier expansion isolate human population random mating
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