I am looking for the most efficient way to fit a noncentral chi-squared distribution with fixed d.o.f. to a given data set. So the inputs are d.o.f. and the data and the output should be the noncentrality parameter that gives the best (maximum likelihood? or any other approach that would be more computationally efficient).
Since on Wikipedia the expression for the noncentral chi2 pdf is an infinite sum of chi2 I am at a bit of a loss as to where to start. Might it be possible to find an analytic MLE for the noncentrality in case of fixed dof? Or any other tricks or cancellations that might simplify the likelihood calculation in this special case.