The cumulative density function of a Rayleigh distribution is (according to the wikipedia) :
So you actually have :
But it looks like you don't have the same definition of the Rayleigh distribution than the wikipedia...
I've a problem regarding Rayleigh pdf.
In particular, I know the ratio between two part of the probability density function, at the right and at the left of a given threshold point , so
and from the former I need to compute the value of the parameter of the Rayleigh distribution .
I've made the first steps, reducing the former in
and solving the definite integral, obtaining
However, is now possible to solve the last equation in ? otherwise, is there any other method to compute (or, at least, estimate) the value of from the first equation?
Thank you in advance for any suggestion!