SimMultiCorrData (version 0.2.0)

pdf_check: Check Polynomial Transformation Constants for Valid Power Method PDF

Description

This function determines if a given set of constants, calculated using Fleishman's Third-Order (method = "Fleishman", 10.1007/BF02293811) or Headrick's Fifth-Order (method = "Polynomial", 10.1016/S0167-9473(02)00072-5) Polynomial Transformation, yields a valid pdf. This requires 1) the correlation between the resulting continuous variable and the underlying standard normal variable (see power_norm_corr) is > 0, and 2) the constants satisfy certain constraints (see Headrick & Kowalchuk, 2007, 10.1080/10629360600605065).

Usage

pdf_check(c, method)

Arguments

c

a vector of constants c0, c1, c2, c3 (if method = "Fleishman") or c0, c1, c2, c3, c4, c5 (if method = "Polynomial"), like that returned by find_constants

method

the method used to find the constants. "Fleishman" uses a third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.

Value

A list with components:

rho_pZ the correlation between the continuous variable and the underlying standard normal variable

valid.pdf "TRUE" if the constants produce a valid power method pdf, else "FALSE"

References

Fleishman AI (1978). A Method for Simulating Non-normal Distributions. Psychometrika, 43, 521-532. 10.1007/BF02293811.

Headrick TC (2002). Fast Fifth-order Polynomial Transforms for Generating Univariate and Multivariate Non-normal Distributions. Computational Statistics & Data Analysis, 40(4):685-711. 10.1016/S0167-9473(02)00072-5. (ScienceDirect)

Headrick TC (2004). On Polynomial Transformations for Simulating Multivariate Nonnormal Distributions. Journal of Modern Applied Statistical Methods, 3(1), 65-71. 10.22237/jmasm/1083370080.

Headrick TC, Kowalchuk RK (2007). The Power Method Transformation: Its Probability Density Function, Distribution Function, and Its Further Use for Fitting Data. Journal of Statistical Computation and Simulation, 77, 229-249. 10.1080/10629360600605065.

Headrick TC, Sawilowsky SS (1999). Simulating Correlated Non-normal Distributions: Extending the Fleishman Power Method. Psychometrika, 64, 25-35. 10.1007/BF02294317.

Headrick TC, Sheng Y, & Hodis FA (2007). Numerical Computing and Graphics for the Power Method Transformation Using Mathematica. Journal of Statistical Software, 19(3), 1 - 17. 10.18637/jss.v019.i03.

See Also

fleish, poly, power_norm_corr, find_constants

Examples

# NOT RUN {
# Chi-squared (df = 1) Distribution (invalid power method pdf)
con <- find_constants(method = "Polynomial", skews = sqrt(8), skurts = 12,
                      fifths = 48*sqrt(2), sixths = 480)$constants
pdf_check(c = con, method = "Polynomial")

# Beta (a = 4, b = 2) Distribution (valid power method pdf)
con <- find_constants(method = "Polynomial", skews = -0.467707,
                      skurts = -0.375, fifths = 1.403122,
                      sixths = -0.426136)$constants
pdf_check(c = con, method = "Polynomial")

# }