# Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll be fine with it.

Suppose that $$\Gamma_i$$ follows a gamma distribution with shape $$\alpha_i$$ and scale $$\beta_i$$. Then $$X = \sum_{i=1}^n \Gamma_i$$ follows a $$GGC_n(\alpha,\beta)$$

Is it possible, knowing $$n$$, to estimate $$\alpha$$ and $$\beta$$ parameters on some dataset ?

• In principle it is, because it's possible to work analytically with the GGC to some extent: see stats.stackexchange.com/questions/72479. My answer there exhibits it as a mixture of Gammas (potentially with negative weights) so, like all mixture-model fitting, expect the results to be extremely uncertain unless both $n$ is very small ($1$ or $2$) and you have a huge amount of data. – whuber Dec 3 '19 at 19:09