# Proper likelihood function of the ratio of two spectra

1. Jan 27, 2015

### QuantumDefect

Hello PF'ers,

I am doing an unbinned likelihood analysis where I am analyzing the ratio of two spectra:
$\frac{S_{1}(E)}{S_{2}(E)} = F(E)$

and each spectra,

$S_{1}, S_{2}$

has its own data set. My first idea was to take the function, $F(E)$ and divide by the integral of the function to get a probability distribution but I am unsure how to input my data. If this was binned, it would be straight forward but in the unbinned case, it has stumped me. Anyone have any ideas? Thanks a bunch!

2. Jan 27, 2015

### Stephen Tashi

What is a likelihood analysis? (I've heard of maximum likelihood estimation and likelihood ratio tests.)

Things dealing with likelihood require a probability model. What is the probability model for you data?