I have a vector that has a non-central chi-squared distribution. How do I estimate its distributional parameters i.e. degrees of freedom $d$ and non-centrality parameter $\lambda$?


It cannot be done accurately according to what the researhes achieved, the best numerical unbiased estimator is (2.8) in the first paper:

Unbiased Estimation in the Non-central Chi-Square Distribution

An Approximation of the Non-central Chi-Square Distribution

Estimation of the Non-Centrality Parameter of a Chi-Square Distribution

I don't think there is an R-package estimating this noncentral parameter, altough I know that fpow can estimate noncentral parameters of F-distributions.


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