Moments of a statistic caused by random combinations or random matings (Q1057031)

Let \(A_{ij}\) be a \(k\times k\) matrix. For a random permutation \(L=(L_ 1, L_ 2,..., L_ k)\) of (1, 2,..., k), taking its all possible k! values with probability 1/k!, the authors define the random variable \(A(L)=k^{-1}\sum A_{iL_ i}\) and compute its first five moments \(M_ j\), \(j=1,...,5\). An application in the study of an isolated human population is demonstrated. Namely, for \(52^ 2\) pairs of males and females the coefficients \(A_{ij}\) of consanguinity, forming a 52\(\times 52\) matrix, are computed. The authors test the hypothesis of ''random combination'' of pairs of males and females, using the moments \(M_ j\), \(j=1,...,5\).