P = ncfcdf(X,NU1,NU2,DELTA) computes the noncentral F cdf 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. NU1, NU2, and DELTA can be vectors, matrices, or multidimensional arrays that have the same size, which is also the size of P. A scalar input for X, NU1, NU2, or DELTA is expanded to a constant array with the same dimensions as the other inputs.

The noncentral F cdf is

where I(x|a,b) is the incomplete beta function with parameters a and b.

Examples

Compare the noncentral F cdf with δ = 10 to the F cdf with the same number of numerator and denominator degrees of freedom (5 and 20 respectively).

x = (0.01:0.1:10.01)';
p1 = ncfcdf(x,5,20,10);
p = fcdf(x,5,20);
plot(x,p,'-',x,p1,'-')

References

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

ncfcdf - Noncentral F cumulative distribution function

Syntax

Description

Examples

References

See Also

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