---
title: "Normal approximation to the Gamma distribution"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575266/Normal%20approximation%20to%20the%20Gamma%20distribution"
format: markdown
---
The Gamma(0*, b*, *a*) distribution returns the "time" we will have to wait before observing *a* independent [Poisson](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575214/) events, where one has to wait on average *b* units of "time" between each event. The "time" to wait before a single event occurs is a Gamma(0,*b,1*) = Exponential(1/*b*) distribution, with mean *b* and standard deviation *b* too. The Gamma(0, *b*, *a*) is thus the sum of *a* independent [Exponential](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575227/)(1/*b*) distributions, so [Central Limit Theorem](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574953/) tells us for sufficiently large *a* (>30, for example), we can make the approximation:

 

Gamma(0*, b*, *a*) » Normal 

![image](media://ba2f0718-3df5-47f1-adf3-03a9f2c1e33c)

> Macro (mathinline)



![image](media://07639f73-d3db-4f56-b8f4-2f505ec14aa0)

 

The Gamma(0*, b,* *a*) distribution has mean and standard deviation equal to *ab* and *a*½*b* respectively, which provides a nice check to our approximation.

 

 

 

 

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