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

obistats.TDist: Student's t-Distribution Implementation

This Go package provides a lightweight implementation of the Student’s t-distribution, commonly used in statistical inference (e.g., hypothesis testing, confidence intervals) when sample sizes are small or population variance is unknown.

Core Components

• TDist struct:
  Represents a t-distribution parameterized by degrees of freedom V.

• PDF(x) method:
  Computes the probability density function at point x, using:

  
    f(x) = \frac{\Gamma\left(\frac{V+1}{2}\right)}{\sqrt{V\pi} \, \Gamma\left(\frac{V}{2}\right)} 
           \left(1 + \frac{x^2}{V} \right)^{-\frac{V+1}{2}}
  

  Leverages lgamma for numerical stability in Gamma function evaluation.

• CDF(x) method:
  Computes the cumulative distribution function:

  • Returns 0.5 at symmetry point (x == 0);
  • Uses the regularized incomplete beta function mathBetaInc for x > 0;
  • Exploits symmetry: CDF(-x) = 1 − CDF(x) for x < 0.

• Bounds() method:
  Returns a practical truncation interval [-4, 4], sufficient for most visualizations or numerical integration over the central mass of the distribution.

Dependencies & Notes

• Relies on standard library math and custom/internal helpers (lgamma, mathBetaInc) — likely from a shared internal module.
• Designed for performance and numerical robustness, suitable in statistical tooling or benchmark analysis (as suggested by the obistats package name and reference to a bench-related repo).