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

morie_rank_placements(x = rnorm(50), y = rnorm(50))
#> $placements
#>  [1] 23 32 15 37  9 11 44 11 32 19 32 45 45 20  0 50 36 36 28 35 23 32 19  7 39
#> [26] 45 21  8 36 26  1 28 15 19  9 45 20  3 30 32 11  0 15 36 26 25 36  9 42 28
#> 
#> $ranks_y
#>  [1]  45  64  28  79  16  21  89  22  66  36  65  93  92  40   2 100  77  73  55
#> [20]  71  46  67  35  12  82  91  42  14  76  52   4  57  30  37  18  94  39   7
#> [39]  60  63  23   1  29  75  51  49  74  17  86  56
#> 
#> $U_y
#> [1] 1246
#> 
#> $E_U
#> [1] 1250
#> 
#> $Var_U
#> [1] 21041.67
#> 
#> $m
#> [1] 50
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "Rank placements"
#>