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. <br />
Wolfram lists the pdf as being proportional to $$x^{a-1} \exp{-\frac{x}{b}}$$ <https://reference.wolfram.com/language/ref/GammaDistribution.html><br /><br />
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
[![formula][1]][1]
<!-- source: http://oi65.tinypic.com/2ex3gnt.jpg -->
 [1]: https://i.sstatic.net/HeKaN.png