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Eric Coissac
8c7017a99d
- Update obioptions.Version from "Release 4.4.29" to "/v/ Release v5" - Update version.txt from 4.29 → .30 (automated by Makefile)
34 lines
1.6 KiB
Markdown
34 lines
1.6 KiB
Markdown
# Statistical Functions in `obistats` Package
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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.
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## Core Functions
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- **`mathBeta(a, b)`**
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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.
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- **`lgamma(x)`**
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Wrapper around `math.Lgamma`, returning the natural logarithm of the absolute value of the gamma function.
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- **`mathBetaInc(x, a, b)`**
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Computes the *regularized incomplete beta function* $ I_x(a,b) $. This is essential for computing cumulative distribution functions (CDFs) of the beta, F-, and t-distributions.
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- Uses *continued fraction evaluation* (via `betacf`) for accuracy.
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- Applies symmetry transformation ($ x \to 1-x $) when beneficial (per Numerical Recipes).
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- Returns `NaN` for invalid inputs (`x < 0 || x > 1`).
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- **`betacf(x, a, b)`**
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Implements the continued fraction expansion of $ I_x(a,b) $.
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- Iteratively evaluates recurrence relations for even/odd terms.
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- Uses `epsilon = 3e-14` and `maxIterations = 200` for convergence.
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- Handles near-zero denominators via `raiseZero`.
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## Use Cases
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- Statistical hypothesis testing (e.g., Fisher’s exact test).
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- Beta, binomial proportion confidence intervals.
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- F-test and Student's t-distribution CDF computations.
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## Implementation Notes
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Based on *Numerical Recipes in C*, §6.4, with robustness enhancements for floating-point edge cases.
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