I need values for the parameters $ \alpha,\beta$ of a Gamma distribution that represent the parameter $\theta$ in a Poisson distribution,so its expected value.

I'm using these distribution to simulate the number of claims for a portfolio of insureds in the contest of Motorvehicle Insurance.

The only bond for those parameters is that the expectation for the Gamma must be $$ \frac \alpha \beta = 0.069 $$ but there's no costraint about variability so the Method of Moments can't be used.

Does anybody have clues about if there's a standard for these parameters or there's a commonly accepted constant value for the variability of the mean inside a portfolio of risks (for claim numbers)?


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