Chi-squared distribution

ChiSquared(d)

The ChiSquared distribution with «d» degrees of freedom describes the distribution of a Chi-Squared metric defined as

[math]\displaystyle{ \Chi^2 \sum_{i=1}^n {y_i}^2 }[/math]

where each y_i is independently sampled from a standard normal distribution and d = n - 1 . The distribution is defined over nonnegative values.

The Chi-squared distribution is commonly used for analyses of second moments, such as analyses of variance and contingency table analyses. It can also be used to generate the F distribution.

Suppose

Variable V := ChiSquared(k)

Variable W := ChiSquared(m)

Variable S := (V/k)*(W/m)

S is distributed as an F distribution with k and m degrees of freedom.

The F distribution is useful for the analysis of ratios of variance, such as a one-factor between-subjects analysis of variance.

Library

Distributions

See Also

• Dens_ChiSquared
• CumChiSquared
• Normal
• Rayleigh
• Parametric continuous distributions
• Distribution Densities Library