We can estimate the period *t* that has elapsed if we know λ and the number of events *a* that have occurred in time *t*. The mathematics are exactly the same as the estimate for λ. The reader may like to verify that, by using a prior of *p*(*t)* = 1/ *t* we obtain a posterior distribution: *t* = Gamma(1/λ*,α*) which is the same result we would obtain if we were trying to predict forward (i.e. determine a distribution of variability of) the time required to observe *a* events given λ = 1/β. Also, if we can reasonably describe our prior belief of the elapsed period t with a Gamma(b,a) distribution, the posterior is given by a Gamma(b/ (1 + bλ*),**α* + *a*) distribution.

Note that here we use the parameterization Gamma(b, a) *where* *b* *= Scale and* *a =* *Shape, *whereas in other sections of ModelAssist we might report a three-parameter version of the Gamma distribution.