Returns the limiting distribution of n(g(ˉXn)g(μ)) under the Delta Method. For a univariate distribution, this is N(0,g(μ)2σ2). For a multivariate distribution with Jacobian J=Dg(μ), this is MVN(0,JΣJT).

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)
#> [1] 0
vcov(z)
#> [1] 7.389056