SummaryConsideration of the number of events in a Poisson process in excess of a threshold valuer, when it is assumed that at leastrevents do occur, leads to the Displaced Poisson Distribution. The recurrence relationship between successive probabilities is a simple generalization of that of the Poisson distribution. Accordingly the fitting of the distribution to data is straightforward, using either a desk machine or computer.It is a highly flexible unimodal distribution catering for both under‐ and over‐dispersed data and generally fits Poisson type data well. Its properties have been discussed, moment and maximum likelihood estimators for the cases,rknown and unknown have been given, together with several numerical examp