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Binomial inference: PMF, MLE variance, Wilson interval, true confidence

Source: R/acd_native.R
morie_binomial_inference.Rd

Equations 1.1, 1.3, 1.4, 1.6 of Bilder & Loughin (2025).

Usage

morie_binomial_inference(w, n, p = NA, z = 1.96, interval_fn = NULL)

Arguments

w

Successes.

n

Trials.

p

Probability.

z

Normal critical value.

interval_fn

Function(w, n) returning c(lower, upper) for the true-confidence-level sum; NULL skips it.

Value

List with pmf, var_mle, wilson (estimate/lower/upper), and true_level when interval_fn is given.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_binomial_inference(V, V)
#> $var_mle
#> [1] 0 0 0 0 0 0 0 0
#> 
#> $wilson
#> estimate1 estimate2 estimate3 estimate4 estimate5 estimate6 estimate7 estimate8 
#> 0.6032716 0.6711860 0.7192470 0.7550500 0.7827543 0.8048285 0.8228306 0.8377922 
#>    lower1    lower2    lower3    lower4    lower5    lower6    lower7    lower8 
#> 0.2065433 0.3423720 0.4384939 0.5101000 0.5655085 0.6096570 0.6456612 0.6755844 
#>    upper1    upper2    upper3    upper4    upper5    upper6    upper7    upper8 
#> 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
#>