a particular estimation problem.
I'm considering a Poisson distribution and I need to estimate it's parameter knowing the ratio 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 the following
for a given .
Some ideas to solve this?
Thanks in advance!
This start is certainly more clever than the work I've done until now...
anyway, from this point, the only thing I can do is solve the equation in
(where is the "upper" incomplete gamma function).
At this point, for me, is quite impossible to solve the previous for
In your opinion there are other way to simplify the series of the first post???
Thanks for tour attention!
to manage the last equation is possible to see that
is, actually, the same as
where is the gamma regularized function. Even if it is not a "clean" approach, it can be numerically inverted thanks to theBoost C++ Libraries through the gamma_q_inv(.) function giving
I know, it is not a great solution...but is more than nothing
Thank you all!