Estimating the mean of an Exponential distribution using Classical statistics

Download a pdf copy of this help file  here

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: