ABSTRACT
In the univariate case, the Poisson distribution arises in several ways. One is as the limit of the binomial distribution when the index parameter is allowed to go to infinity and the probability of success tends to become small with a restriction on the mean being fixed. Perhaps, a more realistic way of generating the distribution is to consider physical processes in which two conditions hold: changes are homogeneous in time and the future changes are independent of the past experience. In other words, the process is such that the probability of the event of interest remains constant over intervals of the same length, unaffected by the location of the interval and the past history of the process. Under these assumptions the probability distribution of the random variable measuring the number of times the event of interest has occurred in an interval of specified length can be shown to have the Poisson distribution. For an excellent discussion of the various situations in which the distribution arises we refer to Feller (1959).
