I am doing a simulation, and as an input, I need to add 1 more minute to the already existing Gamma Distribution that I have (Alpha = 2.58 and Beta = 24.5). What would my new alpha and beta values be?
I have regular customers that come at the restaurant and are serviced by experienced servers as a gamma distribution (alpha=2.58 and beta=24.5). If they are serviced by inexperience servers, then it takes 1 minute more to service. Considering I have all inexperienced servers serving one day, how will my alpha and beta values change?
Would someone please help me out with this?
In the $\alpha$-$\beta$ parametrization of the Gamma distribution, neither $\alpha$ nor $\beta$ are location parameters. You can see this from the mean of the distribution, which is $\alpha/\beta$. If you modify the distribution by changing $\alpha$ to $\alpha + \beta$, but keeping $\beta$ the same, then the mean increases by 1, but the new distribution is not purely a shift by one unit of the previous distribution, because $P(0<X<1)$ is never zero for a gamma distribution. This may be sufficient for your purposes.