Non-Central F Distribution
X ~ F_(d1,d2)(λ)
Noncentral / Ratio-of-Chi-Squares Family • Published July 22, 2026
The standard distribution behind ANOVA and regression F-test power calculations: a Poisson-mixture of rescaled already-published F densities built directly from the already-published non-central Chi-Square's own construction, with an exact λ=0 tie back to the already-published (central) F confirmed numerically, verified mean/variance formulas, no closed-form maximum-likelihood system, and simulation via a ratio of non-central to central Chi-Squares.
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About This Reference Sheet
The standard distribution behind ANOVA and regression F-test power calculations: a Poisson-mixture of rescaled already-published F densities built directly from the already-published non-central Chi-Square's own construction, with an exact λ=0 tie back to the already-published (central) F confirmed numerically, verified mean/variance formulas, no closed-form maximum-likelihood system, and simulation via a ratio of non-central to central Chi-Squares.
Support
x ∈ [0, ∞)
Parameters
d1 > 0 (numerator df), d2 > 0 (denominator df), λ ≥ 0 (noncentrality)