Choice and Order: An Extension to Kendall's tau
David C. Blest · Journal of the Royal Statistical Society Series D (The Statistician) · 1999
This paper offers an extension of Kendall's measure τ of the extent of disarray of a permutation of originally ordered data. As in Kendall's work the analysis is based on the number of transpositions that are required to return to the original order. The focus here is on the cases where a limited number only of the original set is selected and reordered. For each integer n≥ 4 an apparently new set of integer sequences representing the frequency of permutations of m≤n− 1 chosen items requiring a given number of transpositions is obtained. These when added in the indicated manner yield the frequencies offered by Kendall. For large n and m it is shown that the distribution of relative frequencies approaches a normal distribution for sufficiently large m, effectively for m≥ 10.