Binomial-Poisson approx for np, p small
MTB > pdf;
SUBC> poisson 1.

    POISSON WITH MEAN =   1.000
       K          P( X = K)
       0            0.3679
       1            0.3679
       2            0.1839
       3            0.0613
       4            0.0153
       5            0.0031
       6            0.0005
       7            0.0001
       8            0.0000
MTB > pdf;
SUBC> binomial 1000 .001.

    BINOMIAL WITH N =1000  P = 0.001000
       K          P( X = K)
       0            0.3677
       1            0.3681
       2            0.1840
       3            0.0613
       4            0.0153
       5            0.0030
       6            0.0005
       7            0.0001
       8            0.0000


Agresti Table 1.1 p.5

MTB > pdf;                         MTB > pdf ;
SUBC> poisson 2.                   SUBC> binomial 10 .2.

Probability Density Function       Probability Density Function      
                                                                     
Poisson with mu = 2.00000          Binomial with n = 10 and p = 0.20 
                                                                     
         x      P( X = x)            x      P( X = x)         
         0        0.1353             0        0.1074          
         1        0.2707             1        0.2684          
         2        0.2707             2        0.3020          
         3        0.1804             3        0.2013          
         4        0.0902             4        0.0881          
         5        0.0361             5        0.0264          
         6        0.0120             6        0.0055          
         7        0.0034             7        0.0008          
         8        0.0009             8        0.0001          
         9        0.0002             9        0.0000          
        10        0.0000     
                                    
match less good.                                    





















