Check probability function of a multivariate Fisher's noncentral hypergeometric distribution

Density_FMVNCHypergeo.R

library(BiasedUrn)
softmax <- function(x){
  mx = max(x)
  ex = exp(x-mx)
  ex/sum(ex)
}

MVNCH_Fisher <- function(K,M,OR){
  CB = combn(K,M)
  nr = ncol(CB)
  X = matrix(0, nr, K)
  for(i in 1:nr){
    X[i, CB[,i]]=1  
  }
  prob = softmax(X%*%log(OR))
  list(X=X, prob = prob)
}

K=10
set.seed(123); OR = rexp(K)
M=3

dist_F = MVNCH_Fisher(K,M,OR)
theo_F = numeric(nrow(dist_F$X))
for(i in 1:nrow(dist_F$X)){
  theo_F[i] = dMFNCHypergeo(x = dist_F$X[i,], m = rep(1, K), n=M, odds = OR)
}

plot(dist_F$prob, theo_F)
abline(0, 1, lty=2)