Fmean: Edgeworth expansion for standardized mean

In innager/edgee: Edgeworth Expansions and Higher-Order Inference

Edgeworth expansion for standardized mean

Description

Calculate values of 1 - 4-term Edgeworth expansions (EE) (2nd - 5th order) for the standardized mean.

Usage

Fm1(x, n, lam)

Fm2(x, n, lam)

Fm3(x, n, lam)

Fm4(x, n, lam)

Arguments

x	numeric vector of quantiles of sampling distribution.
n	sample size.
lam	a vector of scaled cumulants or their estimates, starting with 3rd (skewness). Term 1 needs a third cumulant only, term 2 - third and fourth (kurtosis), and so on.

Details

Higher-order approximations of the cumulative distribution function of the standardized sample average.

Value

A vector of the same length as x containing the values of Edgeworth expansion of a corresponding order (Fm1 for a 1-term or 2nd order EE, Fm2 for a 2-term EE, and so on).

See Also

Fdiff for EE for two-sample standardized difference in means and pfuns for p() functions used in EE terms.

Examples

# Gamma distribution with shape parameter shp
n <- 10
shp <- 3
ord <- 3:6                # orders of scaled cumulants
lambdas <- factorial(ord - 1)/shp^((ord - 2)/2)
x <- seq(2, 5, by = 0.5)  # thicker tail
1 - Fm1(x, n, lambdas)

innager/edgee documentation built on April 24, 2024, 8:14 p.m.