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Miha Kralj
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lib/numerics/fdist/Fdist.md
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| **PineScript** | [fdist.pine](fdist.pine) |
- The F-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the F-distribution (Fisher-Snedecor distr...
- Parameterized by `d1` (default 1), `d2` (default 1), `period` (default 14).
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Trading note:** F-distribution; used in ANOVA and regression significance tests. Compares model variances.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The F-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the F-distribution (Fisher-Snedecor distribution), producing an output in $[0, 1]$. The F-distribution arises as the ratio of two chi-squared random variables divided by their respective degrees of freedom, making it the natural distribution for variance ratio tests. By mapping normalized price through the regularized incomplete beta function with parameters tied to degrees of freedom $d_1$ and $d_2$, FDIST provides a probabilistic ranking that is asymmetric: the CDF shape changes qualitatively depending on whether $d_1 < d_2$, $d_1 = d_2$, or $d_1 > d_2$, giving traders control over the nonlinear response curve.
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- Snedecor, G.W. "Calculation and Interpretation of Analysis of Variance and Covariance." Collegiate Press, 1934.
- Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing." 3rd edition, Cambridge University Press, 2007. Chapter 6.4 (Incomplete Beta Function).
- Lo, A. & MacKinlay, A.C. "Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test." Review of Financial Studies, 1988.
- Lentz, W.J. "Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions." Applied Optics, 1976.
- Lentz, W.J. "Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions." Applied Optics, 1976.