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- .claude/CLAUDE.md - .claude/commands/subagentes.md - .claude/rules/INDEX.md - .mcp.json - bash/functions/cybersecurity/analyze_dns.md - bash/functions/cybersecurity/audit_http_headers.md - bash/functions/cybersecurity/audit_ssh_config.md - bash/functions/cybersecurity/check_firewall.md - bash/functions/cybersecurity/detect_suspicious_users.md - bash/functions/cybersecurity/encrypt_file.md - ... Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
76 lines
3.2 KiB
Markdown
76 lines
3.2 KiB
Markdown
---
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name: beta_dist
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kind: function
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lang: cpp
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domain: datascience
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version: "1.0.0"
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purity: pure
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signature: "double lgamma_lanczos(double x); double log_beta(double a, double b); double beta_pdf(double x, double a, double b); double beta_cdf(double x, double a, double b); double beta_quantile(double p, double a, double b); double beta_mean(double a, double b); double beta_variance(double a, double b); double beta_std(double a, double b)"
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description: "Distribucion Beta(a,b) completa: log-Gamma (Lanczos), log B(a,b), pdf, cdf (incomplete beta via continued fraction), quantile (bisection), mean/var/std. Para inferencia Bayesiana Beta-Binomial (mcmc-bayes / mcmc-full)."
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tags: [beta, distribution, bayesian, lgamma, incomplete_beta, datascience, pendiente-usar]
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uses_functions: []
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uses_types: []
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returns: []
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returns_optional: false
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error_type: ""
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imports: [cmath]
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tested: false
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tests: []
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test_file_path: ""
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file_path: "cpp/functions/datascience/beta_dist.cpp"
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params:
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- name: x
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desc: "Soporte de la distribucion en [0, 1]. Fuera devuelve 0 (pdf) o se clamp (cdf)."
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- name: a
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desc: "Parametro alpha (>0)."
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- name: b
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desc: "Parametro beta (>0)."
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- name: p
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desc: "(quantile) Probabilidad en [0, 1]."
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output: "Escalares double. Precision: lgamma ~1e-15, cdf ~1e-12, quantile ~1e-7. log_beta y beta_pdf computados en log-space para evitar overflow con a/b grandes."
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---
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# beta_dist
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Pack completo para inferencia Beta-Binomial. Soporta los 3 calculadores Bayesianos del set (mcmc-bayes, mcmc-full, y el targetPDF de mcmc-lab si se cambia a Beta).
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## Algoritmos
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| Funcion | Algoritmo | Precision |
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|---|---|---|
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| `lgamma_lanczos` | Lanczos g=7, n=9 + reflection x<0.5 | ~1e-15 |
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| `beta_pdf` | log-space exp((a-1)*log(x) + (b-1)*log(1-x) - log B) | full fp64 |
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| `beta_cdf` | I_x(a,b) via continued fraction (NR 6.4) | ~1e-12 |
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| `beta_quantile` | bisection (60 iter, tol 1e-7) | ~1e-7 |
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| `beta_mean/var/std` | formulas cerradas | exacto modulo fp |
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## Uso (Bayesian inference)
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```cpp
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// Posterior Beta(alpha + k, beta + n - k) tras k exitos en n trials con
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// prior Beta(alpha, beta).
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double a_post = alpha + k;
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double b_post = beta + (n - k);
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double map = (a_post - 1.0) / (a_post + b_post - 2.0); // moda
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double mean = fn::ds::beta_mean(a_post, b_post);
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double std = fn::ds::beta_std (a_post, b_post);
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// CI 95% via quantiles
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double lo = fn::ds::beta_quantile(0.025, a_post, b_post);
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double hi = fn::ds::beta_quantile(0.975, a_post, b_post);
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// Densidad para plotear
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for (int i = 0; i <= 100; ++i) {
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double x = i / 100.0;
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double y = fn::ds::beta_pdf(x, a_post, b_post);
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// ... feed a line_plot
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}
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```
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## Notas
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- La continued fraction converge en <50 iteraciones para `a, b` razonables (<1000); para parametros muy grandes (>1e4) considerar regularized incomplete beta de la libreria estandar — pero `std::lgamma` no esta garantizado portable bit-exact entre toolchains, por eso esta implementacion es self-contained.
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- `beta_quantile` es bisection puro: ~60 iter siempre, robusto pero no maximalmente eficiente. Newton encadenado a `beta_cdf` y `beta_pdf` daria 5-10 iter pero requiere care con los bordes.
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- Para `a < 1` o `b < 1` la PDF tiene singularidades en los bordes — la implementacion devuelve 0 estrictamente fuera de (0,1) para evitar inf.
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