Comparison of classic and Bayesian estimate of mean time b in a Poisson process

The classics statistics estimate of b is given by:

where we have observed  n durations (random samples from an Exponential distribution) with mean x.

The Bayesian estimate with a p(b) = 1/b prior, and a likelihood function of VoseGammaProb(n*x,n,b,0) gives a slightly lower estimate than the classic estimate for small n.

 

Mode

Mean

Classic

Bayesian

 

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