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Miha Kralj
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lib/numerics/gammadist/Gammadist.md
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| **PineScript** | [gammadist.pine](gammadist.pine) |
- The Gamma Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the gamma distribution, producing an ...
- Parameterized by `alpha` (default 2.0), `beta` (default 1.0), `period` (default 14).
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Trading note:** Gamma distribution; models waiting times and aggregate claims. Used in risk modeling.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The Gamma Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the gamma distribution, producing an output in $[0, 1]$. The gamma distribution generalizes the exponential distribution by adding a shape parameter $\alpha$ that controls whether the PDF is monotonically decreasing ($\alpha < 1$), exponential ($\alpha = 1$), or bell-shaped with a right skew ($\alpha > 1$). Combined with a rate parameter $\beta$ that scales the normalized input, GAMMADIST provides a flexible nonlinear mapping with controllable asymmetry. The CDF is computed via the regularized lower incomplete gamma function using series expansion or Lentz continued fraction, selecting the faster-converging method based on the argument relative to the shape parameter.
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- Lanczos, C. "A Precision Approximation of the Gamma Function." SIAM J. Numerical Analysis B, 1964.
- Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing." 3rd edition, Cambridge University Press, 2007. Chapter 6.2 (Incomplete Gamma Function).
- Lentz, W.J. "Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions." Applied Optics, 1976.
- Johnson, N.L., Kotz, S. & Balakrishnan, N. "Continuous Univariate Distributions, Vol. 1." Wiley, 1994.
- Johnson, N.L., Kotz, S. & Balakrishnan, N. "Continuous Univariate Distributions, Vol. 1." Wiley, 1994.