The frequency distribution of the trip production from which the conventional triprate is derived as the mean of its distribution is studied for the purpose of building a trip end model. Some notable properties of the frequency distribution of the trip production are investigated, and the relationships between the frequency distribution of the trip production and the potential variables included in the model are explicitly given by the preliminary analysis. Consequently, a model of joint probability distribution of trips and traffic purposes is proposed based on the person trip survey in the North Kyushu districts. Some interesting characteristics of the trip production are also illustrated by use of the proposed model.