Simplifying a probability distribution function using an exponential function

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I have a pdf for a variable $r$ given two other variables $m, \kappa$ defined as follows:

\begin{align} p(r|m,\kappa)=\frac{I_0(\kappa r)}{I_0(\kappa)^m}r\psi_m(r), \end{align}

where $\psi_m(r)$ is some function (not important), and $I_0$ is the modified Bessel function of the first kind with order 0 (also not important).

I'm reading code written by the dude who defined this pdf, but in his code he uses the following equation for it:

\begin{align} p(r|m,\kappa)=e^{I_0(\kappa r) - mI_0(\kappa)}r\psi_m(r). \end{align}

In his code, he then divides the whole function (across all $r$) by its sum.

Can anyone shed some light on how these two forms of the pdf match up?