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Chi-square

Sum of squared standard normals; a gamma special case central to inference.
Type continuousSupport x ≥ 0Family Quadratic forms
Probability densityX = Σ Zᵢ², Zᵢ ~ N(0,1)
continuous

Chi-square in motion

0.05.2101621
Supportx ≥ 0
Mean5
Variance10
Connections

Where the chi-square
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Standard normal← Σ Zᵢ²

A sum of k squared standard normals is Chi-square(k).

TransformationGammaα=k/2, θ=2

Chi-square(k) is Gamma(k/2, 2).

Special caseGamma← α=k/2, θ=2

The chi-square family lies on a gamma parameter slice.

Special case

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The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

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