⬆️ version bump to v4.5

- Update obioptions.Version from "Release 4.4.29" to "/v/ Release v5"
- Update version.txt from 4.29 → .30
(automated by Makefile)

autodoc/docmd/pkg/obistats/beta.md

@@ -0,0 +1,33 @@
+# Statistical Functions in `obistats` Package
+
+This Go package provides high-precision statistical functions for probability distributions, particularly the **regularized incomplete beta function**, used in hypothesis testing and confidence interval calculations.
+
+## Core Functions
+
+- **`mathBeta(a, b)`**  
+  Computes the *complete beta function* $ B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} $ using logarithms of the gamma function (`math.Lgamma`) for numerical stability.
+
+- **`lgamma(x)`**  
+  Wrapper around `math.Lgamma`, returning the natural logarithm of the absolute value of the gamma function.
+
+- **`mathBetaInc(x, a, b)`**  
+  Computes the *regularized incomplete beta function* $ I_x(a,b) $. This is essential for computing cumulative distribution functions (CDFs) of the beta, F-, and t-distributions.  
+  - Uses *continued fraction evaluation* (via `betacf`) for accuracy.
+  - Applies symmetry transformation ($ x \to 1-x $) when beneficial (per Numerical Recipes).
+  - Returns `NaN` for invalid inputs (`x < 0 || x > 1`).
+
+- **`betacf(x, a, b)`**  
+  Implements the continued fraction expansion of $ I_x(a,b) $.  
+  - Iteratively evaluates recurrence relations for even/odd terms.
+  - Uses `epsilon = 3e-14` and `maxIterations = 200` for convergence.
+  - Handles near-zero denominators via `raiseZero`.
+
+## Use Cases
+
+- Statistical hypothesis testing (e.g., Fisher’s exact test).
+- Beta, binomial proportion confidence intervals.
+- F-test and Student's t-distribution CDF computations.
+
+## Implementation Notes
+
+Based on *Numerical Recipes in C*, §6.4, with robustness enhancements for floating-point edge cases.