Rank placements of Y among X order statistics (Gibbons Ch 2.11.3)

For each Y_j: placement P_j = number of X_i less than Y_j. Their sum is the Mann-Whitney U statistic for Y vs X.

Usage

morie_rank_placements(x, y)

Arguments

x, y

Numeric vectors.

Value

Named list: placements, ranks_y, U_y, E_U, Var_U, m, n.

Examples

set.seed(1)
morie_rank_placements(x = rnorm(50), y = rnorm(50))
#> $placements
#>  [1] 30 10 27  4 48 50 13  4 33 17 50 23 36 24  6 26  2 48 25 50 31  6 35  4  4
#> [26] 26 11 24 24 10 10 17 47  2 35 27 45 14 28 26 10 47 47 37 49 33  4 10  4 11
#> 
#> $ranks_y
#>  [1]  63  21  58  10  93  98  31  11  69  38 100  45  75  48  15  53   3  94  51
#> [20]  99  65  16  73  12   8  55  28  47  49  22  24  37  90   4  72  57  86  33
#> [39]  60  54  25  91  89  77  96  68   7  23   9  27
#> 
#> $U_y
#> [1] 1204
#> 
#> $E_U
#> [1] 1250
#> 
#> $Var_U
#> [1] 21041.67
#> 
#> $m
#> [1] 50
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "Rank placements"
#>