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title: "Estimating the mean of an Exponential distribution using Classical statistics"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575363/Estimating%20the%20mean%20of%20an%20Exponential%20distribution%20using%20Classical%20statistics"
format: markdown
---
If we have n observations {x<sub>i</sub>} we believe are drawn from an Exponential distribution, we can use the pivotal method to get an uncertainty distribution for the mean b:

  


The [unbiased](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26586655) estimate of b is just the average of the n observations:

![image](media://e540f5a0-ec5c-4dfd-a1ab-e67149ccd190)

  


  


> Macro (mathblock)

                                                                                                                           (1)

  


but we have the [identity](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575231/):

![image](media://3eb41e0c-98e9-4885-a589-ec9bf83e271a)

  


  


> Macro (mathblock)

  


Taking b out of the [Gamma](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575231/) distribution works because it is just a scalar. Putting this identity into Equation 1, and rearranging for b we get:

![image](media://a0ba3524-b84c-45e8-a299-d00747aa255e)

  


  


> Macro (mathblock)

  


  


  


  


  


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