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Efficient fitting of noncentral chi-squared distribution to data?

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 ...
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Bayesian inference on noncentrality parameters of t- and F-distributions

Suppose I observe a random variable $x$ drawn from a non-central t- or F- distribution, and would like to perform inference on the non-centrality parameter. How would a Bayesian approach this problem? ...