Merge branch 'dev'

lib/numerics/tdist/Tdist.md

@@ -13,9 +13,7 @@
 | **PineScript**   | [tdist.pine](tdist.pine)                       |
 
 - The Student's t-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of Student's t-distribution, produ...
-- Parameterized by `nu` (default 10), `period` (default 14).
-- Output range: Varies (see docs).
-- Requires `period` bars of warmup before first valid output (IsHot = true).
+- **Trading note:** Student's t-distribution; used for hypothesis testing with small samples. Fatter tails than normal.
 - Validated against TA-Lib, Skender, and Tulip reference implementations where available.
 
 The Student's t-Distribution CDF transforms a min-max normalized price into the cumulative distribution function of Student's t-distribution, producing an output in $[0, 1]$. The t-distribution is the normal distribution's heavier-tailed cousin: as degrees of freedom $\nu$ increase, it converges to the Gaussian; at low $\nu$ it accommodates extreme values that the normal distribution would assign negligible probability. The implementation normalizes price to $[0, 1]$, maps to a t-statistic via linear scaling to $[-3, +3]$, then evaluates the CDF through the regularized incomplete beta function. This makes TDIST a robust percentile ranking that is less sensitive to outliers than NORMDIST.
@@ -129,4 +127,4 @@ Dominated by sequential CF solver. Outer loop PLINQ for bulk p-value computation
 - Mandelbrot, B. "The Variation of Certain Speculative Prices." Journal of Business, 1963.
 - Fama, E.F. "The Behavior of Stock-Market Prices." Journal of Business, 1965.
 - Bollerslev, T. "Generalized Autoregressive Conditional Heteroskedasticity." Journal of Econometrics, 1986.
-- Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing." 3rd edition, Cambridge University Press, 2007. Chapter 6.4.
+- Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing." 3rd edition, Cambridge University Press, 2007. Chapter 6.4.