qgen: 'q()' functions for Edgeworth expansion terms - general...

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

q() functions for Edgeworth expansion terms - general version

Description

Calculate values of q(x) used in terms of Edgeworth expansions (EE) for a general version of t-statistic and other test statistics.

Usage

q1k(x, k12, k31, r)

q2k(x, k12, k22, k31, k41, r)

q3k(x, k12, k13, k22, k31, k32, k41, k51, r)

q4k(x, k12, k13, k22, k23, k31, k32, k41, k42, k51, k61, r)

Arguments

x	numeric vector of quantiles of sampling distribution.
k12, k13, k22, k23, k31, k32, k41, k42, k51, k61	cumulant components - values calculated from sample statistics or distribution parameters.
r	sqare root of variance adjustment. The variance adjustment is generally equal to k21.

Details

These functions implement a general version of EE, which can be used for any one- or two-sample t-statistic, as well as for other test statistics. q1k() is used for term 1 (1-term expansion is also referred to as a 2nd order expansion), q2k() for term 2, and so on. Variance adjustment is incorporated in these functions.

Value

A vector of the same length as x.

See Also

Ftgen for corresponding EE values and qfuns for the short version used in EE for ordinary one-sample t-statistic. For automated generalized verions of these functions see makeQx and makeFx.

Examples

# two-sample test
n1 <- 8
n2 <- 10
shp <- 3
smp <- c(rgamma(n1, shape = shp), rnorm(n2))
a <- rep(1:0, c(n1, n2))
stats <- smpStats(smp, a)
for (i in 1:length(stats)) {
  assign(names(stats)[i], stats[i])
}
k12 <- K12two(A, B_x, B_y, b_x, b_y, mu_x2, mu_x3, mu_x4, mu_x5, mu_x6, 
              mu_y2, mu_y3, mu_y4, mu_y5, mu_y6)
k31 <- K31two(A, B_x, B_y, b_x, b_y, mu_x2, mu_x3, mu_x4, mu_x5, mu_x6, 
              mu_y2, mu_y3, mu_y4, mu_y5, mu_y6)
r <- sqrt(K21two(A, B_x, B_y, b_x, b_y, mu_x2, mu_x3, mu_x4, mu_x5, mu_x6, 
                 mu_y2, mu_y3, mu_y4, mu_y5, mu_y6))
x <- seq(-5, -2, by = 0.5) 
q1k(x, k12, k31, r)

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