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Sycorax ♦
Sycorax ♦
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It is well known that a random variable being Gamma distributed with integer shape parameter k$k$ is equivalent to the sum of the squares of k$k$ normally distributed random variables.

But what can I say about a gamma distributed random variable with non-integer k$k$? Is there any other interpretation other than the Gamma distribution at all?

It is well known that a random variable being Gamma distributed with integer shape parameter k is equivalent to the sum of the squares of k normally distributed random variables.

But what can I say about a gamma distributed random variable with non-integer k? Is there any other interpretation other than the Gamma distribution at all?

It is well known that a random variable being Gamma distributed with integer shape parameter $k$ is equivalent to the sum of the squares of $k$ normally distributed random variables.

But what can I say about a gamma distributed random variable with non-integer $k$? Is there any other interpretation other than the Gamma distribution at all?

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stollenm
stollenm
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Is there another interpretation for a Gamma distribution with non-integer shape parameter?

It is well known that a random variable being Gamma distributed with integer shape parameter k is equivalent to the sum of the squares of k normally distributed random variables.

But what can I say about a gamma distributed random variable with non-integer k? Is there any other interpretation other than the Gamma distribution at all?