Mathematical Problems in Engineering
Volume 2005 (2005), Issue 1, Pages 49-59

A filtered renewal process as a model for a river flow

Mario Lefebvre

Département de Mathématiques et de Génie Industriel, École Polytechnique, C.P. 6079, Succursale Centre Ville, Montréal H3C 3A7, Québec, Canada

Received 13 July 2004

Copyright © 2005 Mario Lefebvre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Various models, based on a filtered Poisson process, are used for the flow of a river. The aim is to forecast the next peak value of the flow, given that another peak was observed not too long ago. The most realistic model is the one when the time between the successive peaks does not have an exponential distribution, as is often assumed. An application to the Delaware River, in the USA, is presented.