I am an electrical engineer who is currently working with some probability problem. In my expression, I experience some numerical error for large $m$ and $n$ and dont now how to overcome it. Paritcularly for evaluating this expression.
$m\sum\limits_{k = 2}^n ( 1 - {(1 - kq{p^{n - 1}})^{m - 1}})\left( \begin{array}{c} n\\ k \end{array} \right){q^k}{p^{n - k}}$
Where $p$ is a probability and $q=1-p$ and the varibles $m$ and $n$ are both positive integers.
I have a guts feeling that this maybe possible through the use of the log sum exp trick because the expression in the summation is just a bunch of things multiply together but I do not know how.
Would you kindly help me with this.
Thank you for your enthusiasm !