---
title: "Renewal processes"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574992/Renewal%20processes"
format: markdown
---
In a [Poisson process](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574979/), the times between successive events are described by independent identical [Exponential](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575227/) distributions. In a renewal process, like a Poisson process, the times between successive events are independent and identical, but they can take any positive distribution. The Poisson process is thus a particular case of a renewal process.

  


The mathematics of the distributions of number of events in a period (equivalent to the [Poisson distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575214/) for the Poisson process) and the time to wait to observe *x* events (equivalent to the [Gamma](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575231/) distribution in the Poisson process) can be quite complicated, depending on the distribution of time between events. However, [Monte Carlo simulation](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575292/) lets us bypass the mathematics to arrive at both of these distributions.

  


[Example of a renewal process model](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575628/)

  


  


  


  


  


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