I wish to compare the empirical distribution of some (simulated) data with
a non-central chi-squared distribution. (e.g., comparing P-P plots,
histograms,percentiles, percentages (alpha)...)
My problem is calculating the parameters for the non-central chi-squared
distribution from the data.
I have tried taking the first three moments of the non-central chisquared
and solving them as simultaneaous equations to get expressions for
lambda(non-centrality parameter),nu(degrees of freedom) and either C or d
where
C*X^2(nu, lambda) or X^2(nu, lambda) + d
When working with the second of these two I get a negative value for nu or
lambda.
When working with the first, C turns out to be imaginary sometimes
(I tested them by substituting in some previously calculated moments from
simulated data)
So it seems I can't solve the problem this way.
Is there any other way to calculate the parameters of a non-central
chi-squared?
The data I wish to use this method on eventually are likely to be skewed to
the right, possibly with outliers...if that makes a difference.
If anyone has any ideas at all then I'd be very grateful!
Emily Knight
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