Somers'D and ASE - dirty implementation in R

PD    <- c(0.05,0.10,0.50,1,2,5,25)/100
total <- c(5,10,20,25,20,15,5)/100

raw <- rbind(PD,total)*100

defaulted    <- total*PD
nondefaulted <- total*(1-PD)

n <- sum(total)

portfolio <- rbind(defaulted,nondefaulted)/n

portfolio

### ASE

x <- portfolio

wr <- n^2-sum(sapply(1:nrow(x), function(i) sum(x[i,])^2))

A <- function(x,i,j) {

  xr <- nrow(x)
  xc <- ncol(x)

  sum(x[1:xr>i,1:xc>j])+sum(x[1:xr<i,1:xc<j])

}

D <- function(x,i,j) {

  xr <- nrow(x)
  xc <- ncol(x)

  sum(x[1:xr>i,1:xc<j])+sum(x[1:xr<i,1:xc>j])

}

Pf <- function(x) {

  xr <- nrow(x)
  xc <- ncol(x)

  tmp <- NULL

  for (i in 1:xr)
    for (j in 1:xc)

      tmp <- c(tmp,x[i,j]*A(x,i,j))

  sum(tmp)

}

Qf <- function(x) {

  xr <- nrow(x)
  xc <- ncol(x)

  tmp <- NULL

  for (i in 1:xr)
    for (j in 1:xc)

      tmp <- c(tmp,x[i,j]*D(x,i,j))

  sum(tmp)

}

P <- Pf(x)
Q <- Qf(x)

# ASE1
tmp2 <- NULL
for (i in 1:nrow(x))
  for (j in 1:ncol(x))
    tmp2 <- c( tmp2, x[i,j] * ( wr*(A(x,i,j)-D(x,i,j)) - (P-Q)*(sum(x)-sum(x[i,])) )^2 )

# ASE0
tmp <- NULL
for (i in 1:nrow(x))
  for (j in 1:ncol(x))
    tmp <- c( tmp, x[i,j]*(A(x,i,j)-D(x,i,j))^2 )

# Somers' D
# -0.6839158
(P-Q)/wr

# ASE1
# 2.378
2/wr^2*sqrt(sum(tmp2))

# ASE0 - hypothesis of independence
2/wr*sqrt( sum(tmp)-(P-Q)^2/sum(x) )