how to calculate the noncentral chi-square distribution in matlab

To generate random numbers from the noncentral chi-square distribution in MATLAB, we can use the function chi2rnd().

Here's an example of how to generate 1000 random numbers from a noncentral chi-square distribution with 5 degrees of freedom and noncentrality parameter of 1:

main.m
df = 5; % degrees of freedom
ncp = 1; % noncentrality parameter
X = chi2rnd(df, ncp, 1000, 1);
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In this example, df is the degrees of freedom of the distribution, ncp is the noncentrality parameter, and 1000 is the number of random numbers to generate.

We can then calculate various statistics for this distribution, such as the mean, variance, skewness, and kurtosis:

main.m
mu = df + ncp; % mean
variance = 2*(df + 2*ncp); % variance
skewness = sqrt(8/df)*(df + 3*ncp)/sqrt(variance); % skewness
kurtosis = 12/df*(1 + 4*ncp^2/variance); % kurtosis
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These calculations use the formulas for the mean, variance, skewness, and kurtosis of the noncentral chi-square distribution, which can be found in many statistical references.