Efficiency Calculator — Binomial / Poisson / Bayesian

Inputs

Successes (k)

Trials (n)

Alpha prior (Beta shape α)

Beta prior (Beta shape β)

Confidence level (%)

Efficiency estimates

Binomial

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Poisson

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Bayesian (mode)

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Prior distribution

Beta(α, β)

Posterior distribution - Beta(α + k, β + n − k)

mode 0.0000 [0.0000, 0.0000] 0% CL

Binomial error: (1/n)·√(k·(1−k/n)) · Poisson error: √(k/n² + k²/n³) · Bayesian posterior: Beta(α + k, β + n − k), credible interval from the posterior's inverse CDF.