Non Central Chi square distribution function

[Quantinator]

Hi all, I was wondering, what is the best method to calculate the the Non central chi square distribution function?

 

[Daniel Duffy]

What do want to 'calculate'?

 

[Quantinator]

What do want to 'calculate'?

I want to compute the non central chi square distribution and I was wondering, what was the best method to do this?
From my understanding there are various methods such as gamma series method, analytic approximations etc..

 

[Daniel Duffy]

http://www.cs.washington.edu/resear.../dist/stat_tut/weg/nccs_eg/nccs_power_eg.html

 

[Daniel Duffy]

double dof = 3.0;
    double lambda = 1.5;

    boost::math::non_central_chi_squared_distribution<double> myNonCentralChiSquared(dof, lambda);


    cout << "pdf: " << pdf(myNonCentralChiSquared, x) << endl;
    cout << "cdf: " << cdf(myNonCentralChiSquared, x) << endl;

    // Other properties
    cout << "\n***Noncentral Chi^2 Distribution: \n";
    cout << "mean: " << mean(myNonCentralChiSquared) << endl;
    cout << "variance: " << variance(myNonCentralChiSquared) << endl;
    cout << "median: " << median(myNonCentralChiSquared) << endl;
    cout << "mode: " << mode(myNonCentralChiSquared) << endl;
    cout << "kurtosis excess: " << kurtosis_excess(myNonCentralChiSquared) << endl;
    cout << "kurtosis: " << kurtosis(myNonCentralChiSquared) << endl;
    cout << "characteristic function: " << chf(myNonCentralChiSquared, x) << endl;
    cout << "hazard: " << hazard(myNonCentralChiSquared, x) << endl;

 

[Quantinator]

http://www.cs.washington.edu/resear.../dist/stat_tut/weg/nccs_eg/nccs_power_eg.html

Thank you for that,
I think I am a little confused. I think my original question should have been which is the best method to approximate the non central chi square distribution?
Because I am looking for the maths behind it and I have come across many methods etc...

 

[Hob]

Thank you for that,
I think I am a little confused. I think my original question should have been which is the best method to approximate the non central chi square distribution?
Because I am looking for the maths behind it and I have come across many methods etc...

Mathematica and MATLAB both have built in functions, e.g.:

http://www.mathworks.co.uk/help/stats/noncentral-chi-square-distribution.html?refresh=true

I am guessing you want to generate pdf and/or cdf?

 

[Daniel Duffy]

Mathematica and MATLAB both have built in functions, e.g.:

http://www.mathworks.co.uk/help/stats/noncentral-chi-square-distribution.html?refresh=true

I am guessing you want to generate pdf and/or cdf?

In C++

boost::math::non_central_chi_squared_distribution<double> myNonCentralChiSquared(dof, lambda);


5.


6.  double x = 0.5;


7.    cout << "pdf: " << pdf(myNonCentralChiSquared, x) << endl;


8.    cout << "cdf: " << cdf(myNonCentralChiSquared, x) << endl;

 

[Quantinator]

Thanks

 

[yetanotherquant]

Have also a look at R docu:
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Chisquare.html

BTW, there is a short but very clear section on Chi^2 in
"An Introduction to Generalized Linear Models, Second Edition" by Annette J. Dobson