Machine testing for deviation of data from a Poisson distribution

THERE are many situations in which data are obtained describing events that occur at random. If the mechanism causing the random events is such that the events are independent and the probability of occurrence in any given interval of time is constant, the occurrence is described by the Poisson distribution. In a population of events which are normally expected to occur according to the Poisson distribution, certain events may occur as the result of special factors which operate in relation to them only. In such cases, these specially influenced events will not fall within the Poisson distribution that describes the rest of the population. It may be desirable to study the factors causing their peculiar occurrence and this will require that the normally occurring events be separated from the normally occurring ones. A practical machine method for making this kind of separation for any data which are Poisson-distributed is outlined. For clarity, the techniques will be described in terms of a particular example but other applications are of course possible.