* Possion model using d2 method 
* use the data of stata official website
* method d2 requires explicit expression for gradient and Hessian


clear
use http://www.stata-press.com/data/r8/airline
list
gen lnN=ln(n)

* first use canned routine
poisson injuries XYZowned lnN

* user-defined procedure with method d2

program drop _all

program define MLE_d2_poisson
  version 8
  args todo b lnf g negH
  tempvar t1 
  mleval `t1' = `b', eq(1)
  mlsum `lnf'=-exp(`t1')+`t1'*$ML_y1-lngamma($ML_y1+1)               
  if (`todo'==1|`lnf'>=.) exit
  tempname d1
  mlvecsum `lnf' `d1'=-exp(`t1')+$ML_y1, eq(1)
  matrix `g'=(`d1')
  if (`todo'==1|`lnf'>=.) exit
  tempname d11 
  mlmatsum `lnf' `d11'=exp(`t1'), eq(1)
  matrix `negH'=(`d11')
end

ml model d2 MLE_d2_poisson (injuries = XYZowned lnN) 

ml maximize