I am sorry for the poor quality of this question: For $\Gamma(\alpha,\beta)$ random variables, why do we assume $\alpha>0$ and $\beta>0$?
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I don't think the integral of the "density" would converge if the parameters aren't positive (but I may be wrong). – angryavian Jun 12 '21 at 05:53
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Why are you apologising for a the quality of the question when you are the one asking it? – user1729 Jun 18 '21 at 16:12
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The gamma density is the following, for $x>0$
$$f_X(x,a,b)=\frac{b^a}{\Gamma(a)}x^{a-1}e^{-bx}$$
it is easy to prove that its integral cannot converge if $a,b$ are not both positive
tommik
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