obitools4/autodoc/docmd/pkg/obistats/beta.md

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.