Poisson distribution

The poisson distribution is an appropriate model for count data. Examples of such data are mortality of infants in a city, the number of misprints in a book, the number of bacteria on a plate, and the number of activations of a geiger counter. The poisson distribution was derived by the french mathematician Poisson in 1837, and the first application was the describtion of the number of death by horse kicking in the prussian army (Bortkiewicz, 1898).
The poisson distribution is a mathematical rule that assigns probabilities to the number occurences. The probability density function of a Poisson variable is given by

The only thing we have to know to specify the poisson distribution is the mean number of occurences. In the graph the mean number of events is equal to 1/2 From the picture we learn the the probability of zero events .60, the probability of one event is .30, and so on. Generaly, for small values of mu, the distribution is not symmetric but skewed. This is a general property when the mean is small. The distribution becomes more symmetric when the mean is larger. A property of this distribution is that the variance is equal to the mean. The poisson distribution resembles the binomial distribution if the probability of an event is very small

The poisson distribution resembles the binomial distribution if the probability of an event is very small. A poisson regression example is given here. and, here a raking example.