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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 ?

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  • $\begingroup$ 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. $\endgroup$ – whuber Dec 3 '19 at 19:09

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