Ftgen | R Documentation |
Calculate values of 1 - 4-term Edgeworth expansions (EE) (2nd - 5th order) for a general version of t-statistic and other test statistics.
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
)
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 |
norm |
if |
df |
degrees of freedom for Student's t-distribution if |
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.
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).
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
.
# 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)
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