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 \(MVN(0, \Sigma)\).

Provides an algebra over probability distributions enabling
composition, sampling, and automatic simplification to closed forms.
Supports normal, exponential, gamma, Weibull, chi-squared, uniform,
beta, log-normal, Poisson, multivariate normal, empirical, and mixture
distributions with algebraic operators (addition, subtraction,
multiplication, division, power, exp, log, min, max) that automatically
simplify when mathematical identities apply. Includes closed-form MVN
conditioning (Schur complement), affine transformations, mixture
marginals/conditionals (Bayes rule), and limiting distribution builders
(CLT, LLN, delta method). Uses S3 classes for distributions and R6
for support objects.

Alexander Towell

algebraic.dist

Algebra over Probability Distributions

clt function

<dl><dt>base_dist</dt>
<dd>A <code>dist</code> object representing the base distribution.</dd></dl>

Arguments

Central Limit Theorem Limiting Distribution — clt

<dl>

<dt>base_dist</dt>
<dd>A <code>dist</code> object representing the base distribution.</dd>

</dl>

clt: Central Limit Theorem Limiting Distribution

Description

Usage

Value

Arguments

Examples