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If X has a gamma distribution with shape parameter a and rate parameter b, then kX with also be gamma-distributed with rate parameter $\frac{b}{k}$. But this is only true if k is a positive constant.

What if k is a negative constant? Will it then just be equal to the cdf of a gamma-distribution with a positive k, but with a minus in front?

Thomas
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  • What exactly are you asking? cdf won't remain a cdf if a put a minus sign in front. – geetha290krm Mar 14 '23 at 07:37
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