t_cornish_fisher: Cornish-Fisher expansion for Welch's t-statistic

In HuaiyuZhang/tcftt: Two-Sample Tests for Skewed Data

Cornish-Fisher expansion for Welch's t-statistic

Description

This function provides approximation for the quantile function of the sampling distribution of the Welch's t-statistic using Cornish-Fisher expansion (up to second order).

Usage

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

Arguments

p	a probability value.
order	the order of Cornish-Fisher expansion. Valid options are 0, 1, and 2. If set to 0, it reduces to a normal approximation and it returns the p-th percentile of standard normal distribution.
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

Cornish-Fisher expansion value evaluated at p.

Examples

t_cornish_fisher(0.9, order=2,
n1=60, n2=30,
mu1=0, mu2=0,
sigma1=1, sigma2=0.5,
gamma1=1, gamma2=0,
tau1=6, tau2=0)

t_cornish_fisher(0.3, order=1,
n1=60, n2=30,
mu1=0, mu2=0,
sigma1=1, sigma2=0.5,
gamma1=1, gamma2=0,
tau1=6, tau2=0)

HuaiyuZhang/tcftt documentation built on July 9, 2023, 2:52 a.m.