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 \(MVN(0, \Sigma)\).
clt(base_dist)A normal or mvn distribution representing the
CLT limiting distribution.
# CLT for Exp(2): sqrt(n)(Xbar - 1/2) -> N(0, 1/4)
x <- exponential(rate = 2)
z <- clt(x)
mean(z)
#> [1] 0
vcov(z)
#> [1] 0.25