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.
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Azuma, S., Hayashi, K. & Kudô, A. Moments of a statistic caused by random combinations or random matings. Ann Inst Stat Math 36, 475–479 (1984). https://doi.org/10.1007/BF02481986
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DOI: https://doi.org/10.1007/BF02481986