power_norm_corr {SimMultiCorrData}

Calculate Power Method Correlation

Description

This function calculates the correlation between a continuous variable, Y1, generated using a third or fifth- order polynomial transformation and the generating standard normal variable, Z1. The power method correlation (described in Headrick & Kowalchuk, 2007, doi: 10.1080/10629360600605065) is given by: \rho_{y1,z1} = c1 + 3*c3 + 15* c5, where c5 = 0 if method = "Fleishman". A value <= 0 indicates an invalid pdf and the signs of c1 and c3 should be reversed, which could still yield an invalid pdf. All constants should be checked using pdf_check to see if they generate a valid pdf.

Usage

power_norm_corr(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 scalar equal to the correlation.

References

Please see references for pdf_check.

See Also

fleish, poly, find_constants, pdf_check

Examples

# Beta(a = 4, b = 2) Distribution
power_norm_corr(c = c(0.108304, 1.104252, -0.123347, -0.045284, 0.005014,
                      0.001285),
                method = "Polynomial")

# Switch signs on c1, c3, and c5 to get negative correlation (invalid pdf):
power_norm_corr(c = c(0.108304, -1.104252, -0.123347, 0.045284, 0.005014,
                      -0.001285),
                method = "Polynomial")