delta_clt: Delta Method CLT Limiting Distribution

In algebraic.dist: Algebra over Probability Distributions

Delta Method CLT Limiting Distribution

Description

Returns the limiting distribution of \sqrt{n}(g(\bar{X}_n) - g(\mu)) under the Delta Method. For a univariate distribution, this is N(0, g'(\mu)^2 \sigma^2). For a multivariate distribution with Jacobian J = Dg(\mu), this is MVN(0, J \Sigma J^T).

Usage

delta_clt(base_dist, g, dg)

Arguments

base_dist	A dist object representing the base distribution.
g	The function to apply to the sample mean.
dg	The derivative (univariate) or Jacobian function (multivariate) of g. For univariate distributions, dg(x) should return a scalar. For multivariate distributions, dg(x) should return a matrix (the Jacobian).

Value

A normal or mvn distribution representing the Delta Method limiting distribution.

Examples

# Delta method: g = exp, dg = exp
x <- exponential(rate = 1)
z <- delta_clt(x, g = exp, dg = exp)
mean(z)
vcov(z)

algebraic.dist documentation built on Feb. 27, 2026, 5:06 p.m.