t_edgeworth {tcftt}

Edgeworth expansion for Welch's t-statistic

Description

This function provides approximation for the cumulative distribution function of the sampling distribution of the Welch's t-statistic using Normal distribution, first order or second order Edgeworth expansion.

Usage

t_edgeworth(
  x,
  order = 2,
  n1,
  n2,
  mu1,
  mu2,
  sigma1,
  sigma2,
  gamma1,
  gamma2,
  tau1,
  tau2
)

Arguments

x

a real number.

order

the order of edgeworth expansion. Valid options are 0, 1, and 2. If set to 0, it reduces to approximation based on the central limit theorem and returns the CDF of standard normal distribution evaluated at x.

n1

sample size for the sample from the first population.

n2

sample size for the sample from the second population.

mu1

mean of the first population.

mu2

mean of the second population.

sigma1

standard deviation of the first population.

sigma2

standard deviation of the second population.

gamma1

skewness of the first population.

gamma2

skewness of the second population.

tau1

kurtosis of the first population.

tau2

kurtosis of the second population.

Value

Edgeworth expansion evaluated at x.

Examples

t_edgeworth(1.96, order=2,
n1=20, n2=30,
mu1=0, mu2=0,
sigma1=1, sigma2=0.5,
gamma1=1, gamma2=0,
tau1=6, tau2=0)