ncfpdf

Noncentral F probability density function

Syntax

p = ncfpdf(x,nu1,nu2,delta)

Description

p = ncfpdf(x,nu1,nu2,delta) returns the noncentral F probability density function (pdf) with nu1 numerator degrees of freedom, nu2 denominator degrees of freedom, and the noncentrality parameter delta, evaluated at the values in x.

Examples

Compute Noncentral F Distribution Probability Density Function

Compute the probability density function (pdf) of a noncentral F distribution with the numerator degrees of freedom nu1=5, denominator degrees of freedom 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;
nu1 = 5;
nu2 = 20;
delta = 10;
ncf = ncfpdf(x,nu1,nu2,delta);
f = fpdf(x,nu1,nu2);

Plot the noncentral F pdf and the F pdf on the same figure.

figure
plot(x,ncf,"b-",LineWidth=2)
hold on
grid on
plot(x,f,"r--",Linewidth=2)
xlabel("x")
ylabel("p")
legend("Noncentral F pdf","F pdf")
hold off

Input Arguments

x — Values at which to evaluate noncentral F pdf

nonnegative scalar | array of nonnegative scalars

Values at which to evaluate the noncentral F pdf, specified as a nonnegative scalar or an array of nonnegative scalars.

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify one or more of the following input arguments using arrays: nu1, nu2, or delta. If one or more of the input arguments x, nu1, nu2, and delta are arrays, then the array sizes must be the same. In this case, ncfpdf expands each scalar input into a constant array of the same size as the array inputs. Each element in p is the pdf value of the distribution specified by the corresponding elements in nu1, nu2, and delta, evaluated at the corresponding element in x.

Data Types: single | double

nu1 — Numerator degrees of freedom

positive scalar | array of positive scalars

Numerator degrees of freedom, specified as a positive scalar or an array of positive scalars.

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify one or more of the following input arguments using arrays: nu1, nu2, or delta. If one or more of the input arguments x, nu1, nu2, and delta are arrays, then the array sizes must be the same. In this case, ncfpdf expands each scalar input into a constant array of the same size as the array inputs. Each element in p is the pdf value of the distribution specified by the corresponding elements in nu1, nu2, and delta, evaluated at the corresponding element in x.

Data Types: single | double

nu2 — Denominator degrees of freedom

positive scalar | array of positive scalars

Denominator degrees of freedom, specified as a positive scalar or an array of positive scalars.

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify one or more of the following input arguments using arrays: nu1, nu2, or delta. If one or more of the input arguments x, nu1, nu2, and delta are arrays, then the array sizes must be the same. In this case, ncfpdf expands each scalar input into a constant array of the same size as the array inputs. Each element in p is the pdf value of the distribution specified by the corresponding elements in nu1, nu2, and delta, evaluated at the corresponding element in x.

Data Types: single | double

delta — Noncentrality parameter

nonnegative scalar | array of nonnegative scalars

Noncentrality parameter, specified as a nonnegative scalar or an array of nonnegative scalars. When delta=0, the noncentral F distribution is equivalent to the F distribution.

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify one or more of the following input arguments using arrays: nu1, nu2, or delta. If one or more of the input arguments x, nu1, nu2, and delta are arrays, then the array sizes must be the same. In this case, ncfpdf expands each scalar input into a constant array of the same size as the array inputs. Each element in p is the pdf value of the distribution specified by the corresponding elements in nu1, nu2, and delta, evaluated at the corresponding element in x.

Data Types: single | double

Output Arguments

p — Noncentral F pdf values

numeric scalar | numeric array

Noncentral F pdf values, returned as a numeric scalar or array. p is the same size as x, nu1, nu2, and delta after any necessary scalar expansion. Each element in p is the pdf value of the distribution specified by the corresponding elements in nu1, nu2, and delta, evaluated at the corresponding element in x.

Alternative Functionality

• ncfpdf is a function specific to the noncentral F distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, specify the probability distribution name and its parameters. Note that the distribution-specific function ncfpdf is faster than the generic function pdf.

• Use the Probability Distribution Function Tool to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a