The paper I'm getting this from can be found here. It's William Gosset's original derivation of the t-distribution.
I'm interested in the author's use on page 4 of the Pearson Type III distribution for modeling these moments for a new distribution which he found on the previous pages.
He describes the Pearson Type III curve as such:
"The equation referred to an origin at the zero end of the curve ..." (still confused as to what he meant by this) "... will be:"
$y = Cx^pe^{-\gamma x}$, where $\gamma=\frac{M_2}{M_3}$, $p = \frac{4}{\beta_1} - 1$, and $M_2$ and $M_3$ are the 2nd and 3rd moments.
I think I understand the author's motivation for choosing the Type III distribution to build off of using his moments.
My question is about how this form he uses is arrived at given something like the Wikipedia definition of the distribution or the Wolfram Mathworld definition (which seems vaguely similar to the author's definition of a type III curve function). I couldn't really find it mentioned anywhere online and the paper is quite old, so I'm at something of a loss.