Noncentral F PDF
y = distfun_ncfpdf(x,v1,v2,delta)
a matrix of doubles. x is real and x>=0.
a matrix of doubles, numerator degrees of freedom, v1>0 (can be non integer).
a matrix of doubles, denominator degrees of freedom, v2>0 (can be non integer).
a matrix of doubles, the noncentrality parameter, delta>=0
a matrix of doubles, the probability density.
Computes the probability distribution function of the Noncentral F distribution function.
Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.
Caution This distribution is known to have inferior accuracy in some cases.
The Noncentral F distribution has density
for x >= 0 and is zero if x<0.
In the previous equation, the function B(x,y) is the beta function, defined by the equation :
If delta=0, the Noncentral F distribution is equal to the F distribution.
Analysis of the random variable.
If X is a noncentral chi-squared random variable with v1 degrees of freedom, and non centrality parameter delta, Y is a chi-squared random variable with v2 degrees of freedom, therefore the random variable
has a Noncentral F-distribution with parameters v1, delta and v2.
// Test with x scalar, v1 scalar, v2 scalar computed = distfun_ncfpdf(5, 4, 12, 0.3) expected = 0.011247305243159637 // Plot the function h=scf(); x = linspace(0,15,1000); p1 = distfun_ncfpdf(x,10,20,0); p2 = distfun_ncfpdf(x,10,20,1); p3 = distfun_ncfpdf(x,10,20,5); p4 = distfun_ncfpdf(x,10,20,10); p5 = distfun_ncfpdf(x,10,20,40); plot(x,p1,"r") plot(x,p2,"g") plot(x,p3,"b") plot(x,p4,"y") plot(x,p5,"k") legend([ "v1=10, v2=20, delta=0" "v1=10, v2=20, delta=1" "v1=10, v2=20, delta=5" "v1=10, v2=20, delta=10" "v1=10, v2=20, delta=40" ]); xtitle("Noncentral F PDF","x","y"); | ![]() | ![]() |
http://en.wikipedia.org/wiki/Noncentral_F-distribution
http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html