corrZ2corrY {CorrToolBox}

Computation of the Correlation of Bivariate Nonnormal Variables from the Correlation of Bivariate Standard Normal Variables

Description

Fleishman coefficients for each nonnormal continuous variable with the specified skewness and excess kurtosis are found. The Fleishman coefficients and correlation of two standard normal variables are used to find the correlation of the two nonnormal variables as described in Demirtas, Hedeker, and Mermelstein (2012).

Usage

corrZ2corrY(corrZ, skew.vec, kurto.vec)

Arguments

corrZ

The correlation of two standard normal variables.

skew.vec

The skewness vector for continuous variables.

kurto.vec

The kurtosis vector for continuous variables.

Value

The correlation of two continuous nonnormal variables as defined by the skewness and excess kurtosis vectors.

References

Demirtas, H., Hedeker, D., and Mermelstein, R. J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.

Fleishman A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.

See Also

phi2tet

Examples

set.seed(987)
library(moments)

y1<-rweibull(n=100000, scale=1, shape=1)
y1.skew<-round(skewness(y1), 5)
y1.exkurt<-round(kurtosis(y1)-3, 5)

gaussmix <- function(n,m1,m2,s1,s2,pi) {
  I <- runif(n)<pi
  rnorm(n,mean=ifelse(I,m1,m2),sd=ifelse(I,s1,s2))
}
y2<-gaussmix(n=100000, m1=0, s1=1, m2=3, s2=1, pi=0.5)
y2.skew<-round(skewness(y2), 5)
y2.exkurt<-round(kurtosis(y2)-3, 5)

corrZ2corrY(corrZ=-0.849, skew.vec=c(y1.skew, y2.skew), kurto.vec=c(y1.exkurt, y2.exkurt))