Quantile of Marginal K Distribution

Computes the \(p\)-th quantile of the marginal distribution of \(K_J\).

Usage

quantile_K_marginal(p, J, a, b, logS, M = .QUAD_NODES_DEFAULT)

Arguments

p

Numeric; probability level(s) in \([0, 1]\). Can be scalar or vector.

J

Integer; sample size.

a

Numeric; shape parameter of Gamma prior (> 0).

b

Numeric; rate parameter of Gamma prior (> 0).

logS

Matrix; pre-computed log-Stirling matrix.

M

Integer; number of quadrature nodes (default: 80).

Value

Integer vector of quantiles (same length as p). Each element is the smallest \(k\) such that \(P(K_J \leq k) \geq p\).

Details

This is the standard quantile definition for discrete distributions: \(Q(p) = \min\{k : F(k) \geq p\}\).

The function is vectorized over p, allowing efficient computation of multiple quantiles in a single call.

See also

cdf_K_marginal, pmf_K_marginal

Examples

logS <- compute_log_stirling(50)

# Single quantile (median)
quantile_K_marginal(0.5, 50, 1.5, 0.5, logS)
#> [1] 8

# Multiple quantiles at once
quantile_K_marginal(c(0.1, 0.25, 0.5, 0.75, 0.9), 50, 1.5, 0.5, logS)
#> [1]  3  5  8 11 15

# Interquartile range
qs <- quantile_K_marginal(c(0.25, 0.75), 50, 1.5, 0.5, logS)
diff(qs)
#> [1] 6