Noncentral F CDF
p = distfun_ncfcdf(x,v1,v2,delta) p = distfun_ncfcdf(x,v1,v2,delta,lowertail)
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 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X<=x) otherwise P(X>x).
a matrix of doubles, the probability.
Computes the cumulative 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.
// Test with x, v1, v2 scalar computed = distfun_ncfcdf(5,4,12,0.3) expected = 0.98319765219863320 // Plot the function h=scf(); x = linspace(0,15,1000); p1 = distfun_ncfcdf(x,10,20,0); p2 = distfun_ncfcdf(x,10,20,1); p3 = distfun_ncfcdf(x,10,20,5); p4 = distfun_ncfcdf(x,10,20,10); p5 = distfun_ncfcdf(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 CDF","x","$P(X\leq x)$"); | ![]() | ![]() |
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