clt: Central Limit Theorem Limiting Distribution

In algebraic.dist: Algebra over Probability Distributions

Central Limit Theorem Limiting Distribution

Description

Returns the limiting distribution of the standardized sample mean \sqrt{n}(\bar{X}_n - \mu) under the Central Limit Theorem. For a univariate distribution with variance \sigma^2, this is N(0, \sigma^2). For a multivariate distribution with covariance matrix \Sigma, this is MVN(0, \Sigma).

Usage

clt(base_dist)

Arguments

base_dist

A dist object representing the base distribution.

Value

A normal or mvn distribution representing the CLT limiting distribution.

Examples

# CLT for Exp(2): sqrt(n)(Xbar - 1/2) -> N(0, 1/4)
x <- exponential(rate = 2)
z <- clt(x)
mean(z)
vcov(z)

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