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Moments of a statistic caused by random combinations or random matings

  • Shinji Azuma
  • Kenji Hayashi
  • Akio Kudô
Article
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Summary

Given two sets of sizek, {α1...,αk} and {β1...,βk} 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 (α1,βj}. 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 

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References

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1984

Authors and Affiliations

  • Shinji Azuma
    • 1
    • 2
  • Kenji Hayashi
    • 1
    • 2
  • Akio Kudô
    • 1
    • 2
  1. 1.Science University of TokyoTokyoJapan
  2. 2.Kyushu UniversityKyushuJapan

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