Chi-squared PDF
y = distfun_chi2pdf(x,k)
a matrix of doubles, the outcome, greater or equal to zero
a matrix of doubles, the number of degrees of freedom, k>0 (can be non integer)
a matrix of doubles, the probability density.
Computes the probability distribution function of the Chi-squared distribution function.
Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.
The function definition is:
Analysis of the random variable.
If Z1, ..., Zk are independent standard normal random variables, then
has a chi-squared distribution with k degrees of freedom.
// Test with x scalar, k scalar computed = distfun_chi2pdf(4,5) expected = 0.1439759 // Test with expanded x, k scalar computed = distfun_chi2pdf([2 6],5) expected = [0.1383692 0.0973043] // Test with x scalar, k expanded computed = distfun_chi2pdf(4,[4 7]) expected = [0.1353353 0.1151807] // Test with both x,k expanded computed = distfun_chi2pdf([2 6],[3 4]) expected = [0.2075537 0.0746806] // Plot the function h=scf(); k = [2 3 4 6 9 12]; cols = [1 2 3 4 5 6]; lgd = []; for i = 1:size(k,"c") x = linspace(0,10,1000); y = distfun_chi2pdf ( x , k(i) ); plot(x,y) str = msprintf("k=%s",string(k(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("Chi-squared PDF","x","y") legend(lgd); | ![]() | ![]() |
http://en.wikipedia.org/wiki/Chi-squared_distribution