Estimating the mean of an Exponential distribution using Classical statistics


If we have n observations {xi} 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 estimate of b is just the average of the n observations:

                                       (1)

but we have the identity:

                

Taking b out of the Gamma distribution works because it is just a scalar. Putting this identity into Equation 1, and rearranging for b we get:

  

 

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