Ftgen: Standalone Edgeworth expansion for a test statistic - general...

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

Standalone Edgeworth expansion for a test statistic - general case

Description

Calculate values of 1 - 4-term Edgeworth expansions (EE) (2nd - 5th order) for a general version of t-statistic and other test statistics.

Usage

Ft1gen(x, n, k12, k31, r, norm = TRUE, df = NULL)

Ft2gen(x, n, k12, k22, k31, k41, r, norm = TRUE, df = NULL)

Ft3gen(x, n, k12, k13, k22, k31, k32, k41, k51, r, norm = TRUE, df = NULL)

Ft4gen(
  x,
  n,
  k12,
  k13,
  k22,
  k23,
  k31,
  k32,
  k41,
  k42,
  k51,
  k61,
  r,
  norm = TRUE,
  df = NULL
)

Arguments

x	numeric vector of quantiles of sampling distribution.
n	a single value for a sample size summary to be used in Edgeworth expansion. Important: an average (not sum!) of two group sizes for a two-sample test.
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.
norm	if TRUE, normal distribution is used as a base for Edgeworth expansions, if FALSE - Student's t-distribution. Defaults to TRUE.
df	degrees of freedom for Student's t-distribution if norm = FALSE. Provide a single value for the first order approximation (zero term).

Details

Higher-order approximations of the cumulative distribution function of a test statistic. These functions implement a general version of EE that can be used for any one- or two-sample t-statistic as well as for other test statistics.

Value

A vector of the same length as x containing the values of Edgeworth expansion of a corresponding order (Ft1gen for a 1-term or 2nd order EE, Ft2gen for a 2-term EE, and so on).

See Also

qgen for q() functions used in general case EE terms and Ftshort for a short version of EE. For creating EE as a simple function of x, see 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) 
Ft1gen(x, (n1 + n2)/2, k12, k31, r)
Ft1gen(x, (n1 + n2)/2, k12, k31, r, norm = FALSE, df = n1 + n2 - 2)

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