Exact null distributions of Kendall's tau and Spearman's rho

Enumeration over all n! rankings, n <= 8. The exact variances 2(2n+5)/(9n(n-1)) and 1/(n-1) fall out of the pmfs, which is the cross-check. Mirrors morie.fn.gb_kt2/gb_sp2/gb_ktv/gb_spv.

Usage

morie_rank_exact_null(n, statistic = "kendall")

Arguments

n

number of objects, 2..8.

statistic

"kendall" or "spearman".

Value

list: support, pmf, mean, var, var_formula.

References

Gibbons & Chakraborti (2021), Chs. 11.2-11.3.

Examples

morie_rank_exact_null(5, "spearman")$var
#> [1] 0.25