poly {SimMultiCorrData}

Headrick's Fifth-Order Polynomial Transformation Equations

Description

This function contains Headrick's fifth-order polynomial transformation equations (2002, doi: 10.1016/S0167-9473(02)00072-5). It is used in find_constants to find the constants c1, c2, c3, c4, and c5 (c0 = -c2 - 3 * c4) that satisfy the equations given skewness, standardized kurtosis, and standardized fifth and sixth cumulant values. It can be used to verify a set of constants satisfy the equations. Note that there exist solutions that yield invalid power method pdfs (see power_norm_corr, pdf_check). This function would not ordinarily be called by the user.

Usage

poly(c, a)

Arguments

c

a vector of constants c1, c2, c3, c4, c5; note that find_constants returns c0, c1, c2, c3, c4, c5

a

a vector c(skewness, standardized kurtosis, standardized fifth cumulant, standardized sixth cumulant)

Value

a list of length 5; if the constants satisfy the equations, returns 0 for all list elements

References

Headrick TC (2002). Fast Fifth-order Polynomial Transforms for Generating Univariate and Multivariate Non-normal Distributions. Computational Statistics & Data Analysis, 40(4):685-711. doi: 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. doi: 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. doi: 10.1080/10629360600605065.

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. doi: 10.18637/jss.v019.i03.

See Also

fleish, power_norm_corr, pdf_check, find_constants

Examples

# Laplace Distribution
poly(c = c(0.727709, 0, 0.096303, 0, -0.002232), a = c(0, 3, 0, 30))