# fleishman.coef: Computes the coefficients of Fleishman third order... In PoisBinNonNor: Data Generation with Poisson, Binary and Continuous Components

## Description

Computes the coefficients of Fleishman third order polynomials given the marginal skewness and kurtosis parameters of continuous variables.

## Usage

 `1` ```fleishman.coef(n.C, skewness.vec = NULL, kurtosis.vec = NULL) ```

## Arguments

 `n.C` Number of continuous continuous variables. `skewness.vec` Skewness vector for continuous variables. `kurtosis.vec` Kurtosis vector for continuous variables.

## Details

The execution of the function may take some time since it uses multiple starting points to solve the system of nonlinear equations based on the third order Fleishman polynomials. However, since users need to run it only once for a given set of specifications, it does not constitute a problem.

## Value

A matrix of coefficients. The columns represent the variables and rows represent the corresponding a,b,c, and d coefficients.

## 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.

`validation.skewness.kurtosis`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```## Not run: #Consider four continuous variables, which come from #Exp(1),Beta(4,4),Beta(4,2) and Gamma(10,10), respectively. #Skewness and kurtosis values of these variables are as follows: n.C<-4 skewness.vec=c(2,0,-0.4677,0.6325) kurtosis.vec=c(6,-0.5455,-0.3750,0.6) coef.mat=fleishman.coef(n.CN,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec=c(0) kurtosis.vec=c(-1.2) coef.mat=fleishman.coef(n.C,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec1=c(3) kurtosis.vec1=c(5) coef.mat=fleishman.coef(n.C,skewness.vec1,kurtosis.vec1) ## End(Not run) ```