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 search nbvargr (see How can I use the search command to search for programs and get additional help? for more information about using search). 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 pprob pcum |
|------------------------------|
1. | 0 0.13533528 0.13533528 |
2. | 1 0.27067056 0.40600586 |
3. | 2 0.27067056 0.67667639 |
4. | 3 0.18044704 0.85712343 |
5. | 4 0.09022352 0.94734699 |
|------------------------------|
6. | 5 0.03608941 0.98343641 |
7. | 6 0.01202980 0.99546617 |
8. | 7 0.00343709 0.99890327 |
9. | 8 0.00085927 0.99976254 |
10. | 9 0.00019095 0.99995351 |
|------------------------------|
11. | 10 0.00003819 0.99999166 |
+------------------------------+
pprob, mean(2.7) n(10)
Poisson Probabilities for lambda = 2.7
+------------------------------+
| k pprob pcum |
|------------------------------|
1. | 0 0.06720551 0.06720551 |
2. | 1 0.18145488 0.24866039 |
3. | 2 0.24496409 0.49362448 |
4. | 3 0.22046769 0.71409220 |
5. | 4 0.14881569 0.86290789 |
|------------------------------|
6. | 5 0.08036047 0.94326836 |
7. | 6 0.03616221 0.97943056 |
8. | 7 0.01394828 0.99337882 |
9. | 8 0.00470755 0.99808639 |
10. | 9 0.00141226 0.99949867 |
|------------------------------|
11. | 10 0.00038131 0.99987996 |
+------------------------------+