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Construct Target PMF from User Specification

construct_target_pmf.Rd

Creates a target PMF from either a user-provided PMF vector or target moment specification. A supplied PMF must already sum to one; it is validated but never silently normalized. The chi-square constructor explicitly conditions its discretized mass on the declared support and records that provenance.

Usage

construct_target_pmf(J, target)

Arguments

J

Integer; sample size.

target

Either:

  • Numeric vector of length J or J+1: direct PMF specification

  • Named list with mu_K and var_K: construct from moments

Value

A list with components:

pmf

Numeric vector of length J; validated target PMF

mu_K

Target mean

var_K

Target variance

df

(if moments provided) Chi-square degrees of freedom

scale

(if moments provided) Chi-square scale parameter

Details

Direct PMF specification: If target is a numeric vector of length J, it is treated as the PMF for k = 1, ..., J. If length J+1, the k=0 entry must be zero and is dropped.

Moment specification: If target is a list with mu_K and var_K, a discretized chi-square distribution matching these moments is constructed using: $$\text{scale} = \sigma^2_K / (2\mu_K), \quad \text{df} = 2\mu_K^2 / \sigma^2_K$$

See also

discretize_chisq, DPprior_a2_kl

Examples

if (FALSE) { # \dontrun{
# Direct PMF
result <- construct_target_pmf(50, rep(1 / 50, 50))  # Uniform on 1:50

# Moment specification
result <- construct_target_pmf(50, list(mu_K = 5, var_K = 8))
result$mu_K  # 5
result$df    # 6.25

} # }