In reading a research paper I came across this note, I am not sure I fully understand it. I am wondering if they are referring to $P$ as the geometric distribution so their output would be $p^r$ where $p$ is the distribution. Below is my understanding but I am not sure:
The probability of number $r$ is determined by a geometric distribution with parameter $p$ in which $P[r] \sim p^r$. The index $s$ of the synonym chosen given a word is also determined by a another geometric distribution in which $P[s] \sim q^s$.
In further reading, it seems my conclusion was correct. P is the geometric distribution itself $ f(k) = (1-p)^{(k-1)}p$ replacing p with our given number from the paper.