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lib/numerics/betadist/Betadist.md

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 # BETADIST: Beta Distribution CDF
 
+| Property         | Value                            |
+| ---------------- | -------------------------------- |
+| **Category**     | Numeric                        |
+| **Inputs**       | Source (close)                          |
+| **Parameters**   | `period` (default 50), `alpha` (default 2.0), `beta` (default 2.0)                      |
+| **Outputs**      | Single series (Betadist)                       |
+| **Output range** | Varies (see docs)                     |
+| **Warmup**       | `period` bars                          |
+
+### TL;DR
+
+- BETADIST computes the cumulative distribution function of the Beta distribution applied to a min-max normalized price series.
+- Parameterized by `period` (default 50), `alpha` (default 2.0), `beta` (default 2.0).
+- Output range: Varies (see docs).
+- Requires `period` bars of warmup before first valid output (IsHot = true).
+- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
+
 BETADIST computes the cumulative distribution function of the Beta distribution applied to a min-max normalized price series. The source price is first normalized to $[0, 1]$ over a lookback window, then passed through the regularized incomplete beta function $I_x(\alpha, \beta)$ to produce a probability-mapped oscillator. The two shape parameters $\alpha$ and $\beta$ control the nonlinear mapping: symmetric parameters ($\alpha = \beta$) produce a sigmoid-like transformation centered at 0.5, while asymmetric parameters skew the mapping to emphasize extremes in either direction.
 
 ## Historical Context