poisson

#!/bin/awk -f
function logfactorial(n,    f, i){
  f=0
  for(i=1;i<=n;i++){
    f+=log(i)
   }
  return f
}

# m: Mean
# x: Poisson random var
function poisson(m, x,    i, e, TOT, lt, ut){
  e=exp(1)
  for(i=0;i<=x;i++){
    TOT+=exp(-m + i*log(m) - logfactorial(i))
  }
  # Lower tail probability
  lt=TOT
  # Upper tail probability
  ut=1-TOT
  return ut
}

BEGIN{
print poisson(10, 20)
}