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Distfun >> Distfun > Noncentral Chi-Squared > distfun_ncx2pdf

distfun_ncx2pdf

oncentral Chi-squared PDF

Calling Sequence

y = distfun_ncx2pdf(x,k,delta)

Parameters

x :

a matrix of doubles, the outcome, greater or equal to zero

k :

a matrix of doubles, the number of degrees of freedom, k>0 (can be non integer)

delta :

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

y :

a matrix of doubles, the probability density.

Description

Computes the probability distribution function of the Noncentral Chi-squared distribution function.

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

Caution This distribution is known to have inferior accuracy in some cases.

The function definition is:

where is the chi-squared probability density function with k+2i degrees of freedom.

Examples

// Test with x scalar, k scalar
computed = distfun_ncx2pdf(9,5,4)
expected = 0.0756164

// Plot the function
h=scf();
k = [2 2 2 4 4 4];
delta = [1 2 3 1 2 3];
cols = [1 2 3 4 5 6];
lgd = [];
for i = 1:size(k,"c")
x = linspace(0,10,1000);
y = distfun_ncx2pdf ( x , k(i), delta(i));
plot(x,y)
str = msprintf("k=%s, delta=%s",..
string(k(i)),string(delta(i)));
lgd($+1) = str;
end
for i = 1:size(k,"c")
hcc = h.children.children;
hcc.children(size(k,"c") - i + 1).foreground = cols(i);
end
xtitle("Noncentral Chi-squared PDF","x","y")
legend(lgd);

Bibliography

http://en.wikipedia.org/wiki/Chi-squared_distribution

Authors


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