<< distfun_finv F distfun_frnd >>

Distfun >> Distfun > F > distfun_fpdf

distfun_fpdf

F-distribution PDF

Calling Sequence

y = distfun_fpdf(x,v1,v2)

Parameters

x :

a matrix of doubles. x is real and x>=0.

v1 :

a matrix of doubles, numerator degrees of freedom, v1>0 (can be non integer).

v2 :

a matrix of doubles, denominator degrees of freedom, v2>0 (can be non integer).

y :

a matrix of doubles, the probability density.

Description

Computes the probability distribution function of the f distribution function.

Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.

The F distribution has density

for x >= 0 and is zero if x<0.

Analysis of the random variable.

If R1 is a chi-squared random variable with v1 degrees of freedom and R2 is a chi-squared random variable with v2 degrees of freedom, therefore the random variable

has a F-distribution with parameters v1 and v2.

Examples

// Test with x scalar, v1 scalar, v2 scalar
computed = distfun_fpdf(3,4,5)
expected = 0.06817955

// Test with x scalar, v1 scalar, v2 scalar
computed = distfun_fpdf(3,2.5,1.5)
expected = 0.0623281

computed = distfun_fpdf(1.e2,1.e10,1.e-10)
expected = 5.000D-13

// Plot the function
h=scf();
x = linspace(0,5,1000);
p1 = distfun_fcdf(x,1,1);
p2 = distfun_fcdf(x,2,1);
p3 = distfun_fcdf(x,5,2);
p4 = distfun_fcdf(x,100,1);
p5 = distfun_fcdf(x,100,100);
plot(x,p1,"r")
plot(x,p2,"g")
plot(x,p3,"b")
plot(x,p4,"y")
plot(x,p5,"k")
legend([
"v1=1, v2=1"
"v1=2, v2=1";
"v1=5, v2=2"
"v1=100, v2=1"
"v1=100, v2=100"
]);
xtitle("F PDF","x","y");

// See how the distribution goes when
// v1 and v2 are large
scf();
x=linspace(0,2,100);
y=distfun_fpdf(x,1.e1,1.e1);
plot(x,y,"r")
y=distfun_fpdf(x,1.e2,1.e2);
plot(x,y,"g")
y=distfun_fpdf(x,1.e3,1.e3);
plot(x,y,"b")
y=distfun_fpdf(x,1.e4,1.e4);
plot(x,y,"k")
xtitle("F PDF","x","Density")
legend([
"v1=10^1, v2=10^1"
"v1=10^2, v2=10^2"
"v1=10^3, v2=10^3"
"v1=10^4, v2=10^4"
]);

Bibliography

http://en.wikipedia.org/wiki/F-distribution

Catherine Loader, http://svn.r-project.org/R/trunk/src/nmath/df.c

Authors


Report an issue
<< distfun_finv F distfun_frnd >>