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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)
40 lines
2.0 KiB
Markdown
40 lines
2.0 KiB
Markdown
# Beta-Binomial Distribution Implementation in `obistats`
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This Go package provides a complete statistical implementation of the **Beta-Binomial distribution**, a compound discrete probability distribution where the success probability of a Binomial distribution follows a Beta distribution.
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## Core Features
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- **Struct Definition**:
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`BetaBinomial` encapsulates the distribution parameters: number of trials (`N > 0`) and Beta shape parameters `Alpha` and `Beta`, both strictly positive. Optional random source (`Src`) supports reproducible sampling.
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- **Probability Mass Function (PMF)**:
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- `LogProb(x)` computes the natural logarithm of the PMF at integer `x ∈ [0, N]`.
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- `Prob(x)` returns the PMF value via exponentiation.
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- **Cumulative Distribution Function (CDF)**:
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- `LogCDF(x)` evaluates the log-CDF using an analytical expression involving:
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- Log-binomial coefficient (`Lchoose`)
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- Log-beta function (`mathext.Lbeta`)
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- Generalized hypergeometric function `HypPFQ` (via `scientificgo.org/special`).
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- `CDF(x)` returns the standard CDF as `exp(LogCDF(x))`.
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- **Statistical Moments**:
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- Mean: $N \cdot \frac{\alpha}{\alpha + \beta}$
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- Variance: $N \cdot \frac{\alpha \beta (\!N + \alpha + \beta\!)}{(\alpha+\beta)^2 (\alpha+\beta+1)}$
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- Standard deviation: square root of variance.
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- **Mode**:
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Returns the most probable count. Special cases handled:
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- `NaN` if both $\alpha, \beta \leq 1$
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- $0$ if only $\alpha \leq 1$
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- $N$ if only $\beta \leq 1$
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- **Utility Methods**:
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- `LogCDFTable(x)` builds a cumulative log-probability table up to `x`, useful for fast lookup or numerical stability.
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- `NumParameters()` returns the number of distribution parameters (3: $N$, $\alpha$, $\beta$).
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- **Input Validation**:
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Panics on invalid parameters (non-positive `N`, $\alpha$, or $\beta$), ensuring correctness.
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This module supports high-precision statistical computations using specialized mathematical libraries (`gonum.org/v1/gonum/mathext`, `scientificgo.org/special`).
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