eda_sim_old: Simulate data using Fleishman transformation

In mgimond/tukeyedar: Tukey Inspired Exploratory Data Analysis Functions

Simulate data using Fleishman transformation

Description

Generates random data with the specified skewness and excess kurtosis using the Fleishman transformation method.

Usage

eda_sim_old(
  n = 1,
  skew = 0,
  kurt = 0,
  check = TRUE,
  coefout = FALSE,
  coefin = NULL
)

Arguments

n	An integer specifying the number of random data points to generate.
skew	A numeric value specifying the desired skewness of the simulated data.
kurt	A numeric value specifying the desired excess kurtosis of the simulated data.
check	Boolean determining if the combination of skewness and kurtosis are valid.
coefout	Boolean determining if the Fleishman coefficients should be outputted instead of the simulated values.
coefin	Vector of the four coefficients to be used in Fleishman's equation. This bypasses the need to solve for the parameters.

Details

The function uses Fleishman's polynomial transformation of the form:

Y = a + bX + cX^2 + dX^3

where a, b, c, and d are coefficients determined to approximate the specified skewness and excess kurtosis, and X is a standard normal variable. The coefficients are solved using a numerical optimization approach based on minimizing the residuals of Fleishman's equations. An excess kurtosis is defined as the kurtosis of a Normal distribution (k=3) minus 3.

The function is valid for a skewness range of -3 to 3 and an excess kurtosis greater than -1.13168 + 1.58837 * skew ^ 2. If check = TRUE, the function will warn the user if an invalid combination of skewness and kurtosis are passed to the function. Deviation from the recommended combination will result in a distribution that may not reflect the desired skewness and kurtosis values.

If the proper combination of skewness and kurtosis parameters are passed to the function, the output distribution will have a mean of around 0 and a variance of around 1. But note that a strongly skewed distribution will require a large n to reflect the desired properties due to the disproportionate influence of the tail's extreme values on the various moments of the distribution, particularly higher-order moments like skewness and kurtosis.

• Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521–532.

• Wicklin, R. (2013). Simulating Data with SAS (Appendix D: Functions for Simulating Data by Using Fleishman’s Transformation). Cary, NC: SAS Institute Inc. Retrieved from https://tinyurl.com/4tustnph

Value

A numeric vector of simulated data points.

Examples

# Generate a normal distribution
set.seed(321)
x <- eda_sim_old(1000, skew = 0, kurt = 0)
eda_theo(x) # Check for normality

# Simulate distribution with skewness = 1.15 and kurtosis = 2
# A larger sample size is more likely to reflect the desired parameters
set.seed(653)
x <- eda_sim_old(500000, skew = 1.15, kurt = 2)

# Verify skewness and excess kurtosis of the simulated data
# Mean and variance should be close to 0 and 1 respectively
eda_moments(x)

# Visualize the simulated data
hist(x, breaks = 30, main = "Simulated Data", xlab = "Value")

mgimond/tukeyedar documentation built on Feb. 1, 2025, 4:02 a.m.