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] 17 22 17  0  0 12  3 12  7 12 20 41 45 14  4  3 17 22  3 47 14  3  9 16 47
#> [26]  3 22  3 25 41 25 25 12 17 39  4 30 50 17 15 48  9 17 29  7  3  8  9 28 39
#> 
#> $ranks_y
#>  [1]  44  55  48   2   1  32  11  30  19  31  52  86  91  36  15   6  46  57   9
#> [20]  95  37   8  26  41  94  12  56  10  63  85  62  61  33  45  82  14  71 100
#> [39]  47  39  97  25  43  69  20   7  22  24  67  81
#> 
#> $U_y
#> [1] 932
#> 
#> $E_U
#> [1] 1250
#> 
#> $Var_U
#> [1] 21041.67
#> 
#> $m
#> [1] 50
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "Rank placements"
#>