The Poisson process , which is also a renewal process, can be mentioned as an example of a counting process . Some theories can be represented using counting processes. For example, the entire survival time analysis can be represented using the counting process theory.
The result of the then forms a point process on . This positions random points on the positive number line, the distances between which are distributed according to the inter-arrival times. The counting process then runs through the positive numbers at a constant speed and counts how many points it has already hit up to the point in time . Because of this close connection, the counting process and the point process are sometimes used synonymously.