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| **PineScript** | [weibulldist.pine](weibulldist.pine) |
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- The Weibull Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the Weibull distribution, producing...
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- Parameterized by `k` (default 1.5), `lambda` (default 1.0), `period` (default 14).
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- Output range: Varies (see docs).
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- **Trading note:** Weibull distribution; flexible lifetime/reliability model. Used for drawdown duration analysis.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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The Weibull Distribution CDF transforms a min-max normalized price into the cumulative distribution function of the Weibull distribution, producing an output in $[0, 1]$. The Weibull distribution is a flexible two-parameter family that subsumes the exponential distribution ($k = 1$) and approximates the normal distribution ($k \approx 3.6$) as special cases. Its closed-form CDF requires only `pow` and `exp`, making it the computationally cheapest distribution indicator after EXPDIST. The shape parameter $k$ controls the CDF curvature: $k < 1$ produces a concave curve (rapid initial rise), $k = 1$ gives the exponential, $k = 2$ produces the Rayleigh distribution, and $k > 3$ creates an S-shaped curve approaching Gaussian behavior.
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@@ -130,4 +128,4 @@ With SVML: nearly full vectorization. Without SVML: scalar loop but trivially pa
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- Frechet, M. "Sur la loi de probabilite de l'ecart maximum." Ann. Soc. Polon. Math., 1927.
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- Rinne, H. "The Weibull Distribution: A Handbook." CRC Press, 2009.
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- Abernethy, R.B. "The New Weibull Handbook." 5th edition, 2006.
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- Johnson, N.L., Kotz, S. & Balakrishnan, N. "Continuous Univariate Distributions, Vol. 1." Wiley, 1994.
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- Johnson, N.L., Kotz, S. & Balakrishnan, N. "Continuous Univariate Distributions, Vol. 1." Wiley, 1994.
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