Noncentral F probability density function
Y = ncfpdf(X,NU1,NU2,DELTA)
Y = ncfpdf(X,NU1,NU2,DELTA) computes the noncentral F pdf at each of the values in X using the corresponding numerator degrees of freedom in NU1, denominator degrees of freedom in NU2, and positive noncentrality parameters in DELTA. X, NU1, N2, and B can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of Y. A scalar input for P, NU1, NU2, or DELTA is expanded to a constant array with the same dimensions as the other inputs.
The F distribution is a special case of the noncentral F where δ = 0. As δ increases, the distribution flattens like the plot in the example.
Compute the pdf of a noncentral F distribution with degrees of freedom NU1 = 5 and NU2 = 20, and noncentrality parameter DELTA = 10. For comparison, also compute the pdf of an F distribution with the same degrees of freedom.
x = (0.01:0.1:10.01)'; p1 = ncfpdf(x,5,20,10); p = fpdf(x,5,20);
Plot the pdf of the noncentral F distribution and the pdf of the F distribution on the same figure.
figure; plot(x,p1,'b-','LineWidth',2) hold on plot(x,p,'g--','LineWidth',2) legend('Noncentral F','F distribution')
 Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 189–200.