Originally Posted by

**Simo** Dear all,

a particular estimation problem.

I'm considering a Poisson distribution and I need to estimate it's parameter knowing the ratio $\displaystyle k$ between the sum of its values at the left and on the right of a given point. Just to simplify my question, I need to solve for $\displaystyle \lambda$ the following

$\displaystyle \sum_{x=0}^{R-1}\frac{e^{-\lambda}\lambda^{x}}{x!}=k\sum_{x=R}^{\infty}%

\frac{e^{-\lambda}\lambda^{x}}{x!}$

for a given $\displaystyle R$.

Some ideas to solve this?

Thanks in advance!

Simo