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If the sum of two independent random variables is gamma distributed does this imply that the individual random variables are also gamma distributed. I suspect that the answer is no, but I do not know how to construct a counter-example. [The convolution of two gamma distributions with the same scale parameter is also a gamma distribution, but I am dealing with the converse.]

If this can be answered in relation to assuming that the convolution is the exponential distribution f(x) = exp(-x) that would be sufficient for my purposes.

Any help with this would be much appreciated.

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# Deconvolution of gamma distributions

If the sum of two independent random variables is gamma distributed does this imply that the individual random variables are also gamma distributed. I suspect that the answer is no, but I do not know how to construct a counter-example. [The convolution of two gamma distributions with the same scale parameter is also a gamma distribution, but I am dealing with the converse.]

If this can be answered in relation to the exponential distribution f(x) = exp(-x) that would be sufficient for my purposes.

Any help with this would be much appreciated.