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title: "Normal approximation to the Beta distribution"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575264/Normal%20approximation%20to%20the%20Beta%20distribution"
format: markdown
---
The [Beta](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575217/) distribution is difficult to calculate, involving a Beta function in its denominator, so an approximation is often welcome. A [Taylor series](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574961/) expansion of the Beta distribution probability density function shows that the Beta(*a1*,a2,1) distribution can be approximated by the [Normal](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575246/) distribution when *a*1 and a2 are sufficiently large. More specifically, the conditions are:

 

![image](media://9e949d3a-1f97-44f5-a4ce-fee8d385204e)

> Macro (mathblock)

 

A pretty good rule of thumb is that *a*1 and a2 are both equal to 10 or more, but they can be as low as 6 if *a*1 » a2. In such cases, an approximation using the Normal distribution works well where we use the mean and standard deviations from the exact Beta distribution:

 

![image](media://f47dcbae-820f-4656-bd92-30eb018fadfa)

 

> Macro (mathblock)

![image](media://5a4359d8-fa21-40e0-827f-dad4ee74a1ef)

 

Examples of a Normal approximation to a Beta distribution

 

 

 

 

 

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