/* DATE 4\24\91  */
/*     EXACT POISSON PROBABILITY
       Joseph Hilbe - STB       */

program define epoisson
version 2.1
if "%_3"=="" {
  di in re "Type 3 arguments:"
  di in re "     pop ratio  observations   cases"
  exit 198
}
drop _all
quietly {
  set obs %_3
  if (%_3<1) {
     set obs 1
     gen double expect=%_1*%_2
     di in gr "Exact poisson probability => " in ye exp(-expect)
  }
  if (%_3>0)  {
  gen double expect=%_1*%_2
  gen double prob=exp(-expect)
  gen double cum=1
  gen num=[_n-1]+1
    
  while num-1<_N {
    replace cum=cum*num
    replace num=num+1 
  }
  replace prob=(expect^%_3)*(exp(-expect))/cum
  di in gr "Exact poisson probability => " in ye prob
  }
}
drop _all
end