# Moments of a statistic caused by random combinations or random matings

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## Summary

Given two sets of size*k*, {*α*_{1}...,*α*_{k}} and {*β*_{1}...,*β*_{k}} there are*k*! 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.

## Key words

Random combination Gram-Chalier expansion isolate human population random mating## Preview

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## References

- [1]Crow, J. F. and Kimura, M. (1970).
*An Introduction to Population Genetics Theory*, Hamper and Row, New York.zbMATHGoogle Scholar - [2]Elandt Johnson, R. (1971).
*Probability Models and Statistical Method in Genetics*, John Wiley and Sons, New York.zbMATHGoogle Scholar - [3]Hearn, A. C. (1973).
*REDUCE 2 User's Manual Second Edition*, University of Utah.Google Scholar - [4]Kendall, M. G. and Stuart, A. (1977).
*The Advanced Theory of Statistics*, 4th ed., Vol. 1, Charles Griffin, London.zbMATHGoogle Scholar - [5]Nishigaki, I. (1978). Studies on population genetics in the isolates, (VIII) Tomiyama, with special reference to the enzyme activity of polymorphic red cell enzymes,
*Japanese Jour. of Constitutional Medicine*,**42**, 53–89.Google Scholar - [6]Ogawa, J. (1982). The Fisher experimental randomization,
*Jour. Japan Statist. Soc.*,**12**, No. 1, 1–24.MathSciNetzbMATHGoogle Scholar - [7]Schull, W. J. and Neel, J. V. (1965).
*The Effect of Inbreeding on Japanese Children*, Harper and Row, New York.Google Scholar

## Copyright information

© The Institute of Statistical Mathematics, Tokyo 1984