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Nov 14, 2023 at 17:18 comment added jblood94 I instead equated the moments of $e^{-\dot\phi_0}$ with those of $1-\theta_0$, where $\dot\phi_0\sim\text{gamma}(a,b)$ in order to find $a$ and $b$. That way the approximating distribution matches the first two moments of the true distribution of the variable of interest ($\theta_0$).
Nov 14, 2023 at 16:32 history answered JimB CC BY-SA 4.0