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31 lines
1.5 KiB
Markdown
31 lines
1.5 KiB
Markdown
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# `obistats.TDist`: Student's *t*-Distribution Implementation
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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.
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## Core Components
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- **`TDist` struct**:
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Represents a *t*-distribution parameterized by degrees of freedom `V`.
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- **`PDF(x)` method**:
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Computes the *probability density function* at point `x`, using:
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$$
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f(x) = \frac{\Gamma\left(\frac{V+1}{2}\right)}{\sqrt{V\pi} \, \Gamma\left(\frac{V}{2}\right)}
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\left(1 + \frac{x^2}{V} \right)^{-\frac{V+1}{2}}
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$$
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Leverages `lgamma` for numerical stability in Gamma function evaluation.
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- **`CDF(x)` method**:
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Computes the *cumulative distribution function*:
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- Returns `0.5` at symmetry point (`x == 0`);
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- Uses the **regularized incomplete beta function** `mathBetaInc` for `x > 0`;
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- Exploits symmetry: `CDF(-x) = 1 − CDF(x)` for `x < 0`.
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- **`Bounds()` method**:
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Returns a practical truncation interval `[-4, 4]`, sufficient for most visualizations or numerical integration over the central mass of the distribution.
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## Dependencies & Notes
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- Relies on standard library `math` and custom/internal helpers (`lgamma`, `mathBetaInc`) — likely from a shared internal module.
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- 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).
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