Statistics Toolbox

ncfpdf

Noncentral F probability density function

Syntax

• Y = ncfpdf(X,NU1,NU2,DELTA)
  

Description

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. Vector or matrix inputs for X, NU1, NU2, and DELTA must 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 matrix with the same dimensions as the other inputs.

The F distribution is a special case of the noncentral F where  = 0. As increases, the distribution flattens like the plot in the example.

Example

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

• x = (0.01:0.1:10.01)';
  p1 = ncfpdf(x,5,20,10);
  p  = fpdf(x,5,20);
  plot(x,p,'--',x,p1,'-')
  
  
  

References

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

See Also

ncfcdf, ncfinv, ncfrnd, ncfstat, pdf

ncfinv

ncfrnd