Chi-Squared Distribution

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where 𝛤(𝑘) is the Gamma function, and 𝛾(𝑘, 𝑧) is the lower incomplete Gamma function. See Functions below.

Range 0 ≤ 𝑥 ≤ ∞.
Shape parameter 𝜈 > 0, the degrees of freedom.