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distfun >> distfun > Noncentral F Distribution > distfun_ncfrnd

distfun_ncfrnd

Noncentral F random numbers

Calling Sequence

x = distfun_ncfrnd(v1,v2,delta)
x = distfun_ncfrnd(v1,v2,delta,[m,n])
x = distfun_ncfrnd(v1,v2,delta,m,n)

Parameters

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).

delta :

a matrix of doubles, the noncentrality parameter, delta>=0

m :

a 1-by-1 matrix of floating point integers, the number of rows of x

n :

a 1-by-1 matrix of floating point integers, the number of columns of x

x:

a matrix of doubles, the random numbers in the set [0,∞).

Description

Generates random variables from the Noncentral F-distribution function.

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

Examples

x = distfun_ncfrnd(2,5,3)

// Test with expanded v1, v2 and delta
x = distfun_ncfrnd(1:6,1:6,3)

// Check mean and variance
N = 5000;
v1 = 3;
v2 = 5;
delta = 7;
x = distfun_ncfrnd(v1,v2,delta,[1 N]);
RM = mean(x)
RV = variance(x)
[M,V] = distfun_ncfstat(v1,v2,delta)

// Make a plot of the actual distribution of the numbers
v1 = 10;
v2 = 50;
delta = 7;
data = distfun_ncfrnd(v1,v2,delta,1,1000);
scf();
histplot(20,data)
x = linspace(0,4,1000);
y = distfun_ncfpdf(x,v1,v2,delta);
plot(x,y)
xtitle("Noncentral F Random Numbers","X","Density")
legend(["Empirical","PDF"]);

// Make a plot of a ratio of chi-square random numbers
scf();
v1 = 10;
v2 = 50;
delta = 7;
R1 = distfun_ncx2rnd(v1,delta,1,1000);
R2 = distfun_chi2rnd(v2,1,1000);
x = (R1./v1)./(R2./v2);
histplot(20,x)
x = linspace(0,4,1000);
y = distfun_ncfpdf(x,v1,v2,delta);
plot(x,y)
xtitle("$\textrm{Random Numbers }\frac{R_1/v_1}{R_2/v_2}$","X","Density")
legend(["Empirical","PDF"]);

Bibliography

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

Authors


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