Statistics Toolbox™

Chi-Square Distribution

Definition

The χ² pdf is

where Γ( · ) is the Gamma function, and ν is the degrees of freedom.

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Background

The χ² distribution is a special case of the gamma distribution where b = 2 in the equation for gamma distribution below.

The χ² distribution gets special attention because of its importance in normal sampling theory. If a set of n observations is normally distributed with variance σ², and s² is the sample standard deviation, then

This relationship is used to calculate confidence intervals for the estimate of the normal parameter σ² in the function normfit.

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Example

The χ² distribution is skewed to the right especially for few degrees of freedom (ν). The plot shows the χ² distribution with four degrees of freedom.

x = 0:0.2:15;
y = chi2pdf(x,4);
plot(x,y)

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Birnbaum-Saunders Distribution

Copulas