# Parameterization of Gamma Distribution

I have come upon different parameterizations of the Gamma Distribution, but not with regard to shape-scale or shape-rate. It is rather about the sign in the exponent.
Wolfram lists the pdf as being proportional to $$x^{a-1} \exp{-\frac{x}{b}}$$ https://reference.wolfram.com/language/ref/GammaDistribution.html

However, I saw some papers where the minus sign is missing such that, $$x^{a-1}\exp{\frac{x}{b}}$$ From my understanding, both parameters $$a$$ and $$b$$ have to be positive so this must make some kind of difference. Do I have some error in reasoning here?

Edit: Excerpt from a paper

• Could you provide a reference where you actually saw the formula without minus sign..?
– Tim
Commented Sep 16, 2016 at 14:46
• Sure, for instance: Jumps in Equity Index Returns Before and During the Recent Financial Crisis: A Bayesian Analysis (2016, by Kou, Yu and Zhong) on p. 5 in the footnote Commented Sep 16, 2016 at 15:19
• I added a screenshot for clarification. Commented Sep 16, 2016 at 17:19
• This formulation is simply wrong. Have you tried plotting this function..?
– Tim
Commented Sep 16, 2016 at 18:25

$$x^{\alpha - 1} e^{x/\beta} \to 0 \text{ as } x \to 0$$
$$x^{\alpha - 1} e^{x/\beta} \to \infty \text{ as } x \to \infty.$$