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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.


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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.

hold on
legend('Noncentral F','F distribution')

Figure contains an axes. The axes contains 2 objects of type line. These objects represent Noncentral F, F distribution.


[1] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 189–200.

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Introduced before R2006a