Stata FAQ
How can I get poisson probabilities in Stata?

There is an ATS developed program called pprob that will generate a table of poisson probabilities. You can install pprob over the internet by typing findit nbvargr (see How can I use the findit command to search for programs and get additional help? for more information about using findit). Note: pprob is a program called by nbvargr.

Now, let's try the program. First, let's generate a table with a lambda (the mean of a poisson distribution) of 2 and then a table with a lambda of 2.7. In both examples the number of categories will run from 0 to 10.

pprob, mean(2) n(10)

           Poisson Probabilities for lambda = 2

             k       prob    cumprob     invcum 
  1.         0   .1353353   .1353353   .8646647  
  2.         1   .2706706   .4060059   .5939941  
  3.         2   .2706706   .6766764   .3233236  
  4.         3    .180447   .8571234   .1428766  
  5.         4   .0902235    .947347    .052653  
  6.         5   .0360894   .9834364   .0165636  
  7.         6   .0120298   .9954662   .0045338  
  8.         7   .0034371   .9989033   .0010967  
  9.         8   .0008593   .9997625   .0002375  
 10.         9   .0001909   .9999535   .0000465  
 11.        10   .0000382   .9999917   8.34e-06

pprob, mean(2.7) n(10)

           Poisson Probabilities for lambda = 2.7

             k       prob    cumprob     invcum 
  1.         0   .0672055   .0672055   .9327945  
  2.         1   .1814549   .2486604   .7513396  
  3.         2   .2449641   .4936245   .5063756  
  4.         3   .2204677   .7140922   .2859078  
  5.         4   .1488157   .8629079   .1370921  
  6.         5   .0803605   .9432684   .0567316  
  7.         6   .0361622   .9794306   .0205694  
  8.         7   .0139483   .9933788   .0066212  
  9.         8   .0047075   .9980864   .0019136  
 10.         9   .0014123   .9994987   .0005013  
 11.        10   .0003813     .99988     .00012