Data Generation with Count, Binary and Continuous Components

Description

Provides R functions for generation of multiple count, binary and continuous variables simultaneously given the marginal characteristics and association structure. Continuous variables can be of any nonnormal shape allowed by the Fleishman polynomials, taking the normal distribution as a special case.

Details

The package consists of fourteen functions. The functions validation.bin, validation.corr, and validation.skewness.kurtosis validate the specified quantities. correlation.limits returns the lower and upper bounds of pairwise correlations of Poisson, binary and continuous variables. correlation.bound.check validates pairwise correlation values.
intermediate.corr.PP, intermediate.corr.BB, intermediate.corr.CC,
intermediate.corr.PB, intermediate.corr.PC, and intermediate.corr.BC compute intermediate correlation matrix for Poisson-Poisson combinations, binary-binary, continuous-continuous, Poisson-binary, Poisson-continuous, binary-continuous combinations, respectively. The function overall.corr.mat assembles the final correlation matrix. The engine function gen.PoisBinNonNor generates mixed data in accordance with the specified marginal and correlational quantities. Throughout the package, variables are supposed to be inputted in a certain order, namely, first count variables, next binary variables, and then continuous variables should be placed.

Author(s)

Gul Inan, Hakan Demirtas, Ran Gao

Maintainer: Ran Gao <rgao8@uic.edu>

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, (85)15, 3129-3139.

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

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.

Checks if the pairwise correlation among variables are within the feasible range

Description

This function checks if there are range violations among correlation of Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations.

Usage

correlation.bound.check(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, 
coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

References

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

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.

See Also

validation.corr, correlation.limits

Examples

## Not run: 
n.P<-1
n.B<-1
n.C<-1
lambda.vec<-c(1)
prop.vec<-c(0.3)
coef.mat<-matrix(c(-0.3137491,0.8263239,0.3137491,0.0227066),4,1,byrow=F) 
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)
correlation.bound.check(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, 
corr.mat)

n.P<-2
n.B<-2
n.C<-2
lambda.vec<-c(1,2)
prop.vec<-c(0.3,0.5)
coef.mat<-matrix(c(
-0.3137491,  0.0000000,   
 0.8263239,  1.0857433,    
 0.3137491,  0.0000000,
 0.0227066, -0.0294495),4,2,byrow=F)  
corr.mat=matrix(0.8,6,6)
diag(corr.mat)=1
correlation.bound.check(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, 
corr.mat)

## End(Not run)

Computes lower and upper correlation bounds for each pair of variables

Description

This function computes lower and upper limits for pairwise correlations of Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations.

Usage

correlation.limits(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, 
coef.mat = NULL)

Arguments

Details

While the function computes the exact lower and upper bounds for pairwise correlations among binary-binary variables as formulated in Demirtas et al. (2012), it computes approximate lower and upper bounds for pairwise correlations among Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-continuous, and continuous-continuous variables through the method suggested by Demirtas and Hedeker (2011).

Value

The function returns a matrix of size (n.P + n.B + n.C)*(n.P + n.B + n.C), where the lower triangular part of the matrix contains the lower bounds and the upper triangular part of the matrix contains the upper bounds of the feasible correlations.

References

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

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.

See Also

validation.corr, correlation.bound.check

Examples

## Not run: 
n.P<-3
n.B<-2
n.C<-3
lambda.vec<-c(1,2,3)
prop.vec<-c(0.3,0.5)
coef.mat<-matrix(c(
-0.3137491,  0.0000000,  0.1004464, 
 0.8263239,  1.0857433,  1.1050196,  
 0.3137491,  0.0000000, -0.1004464,
 0.0227066, -0.0294495, -0.0400078),4,3,byrow=F)  

#Correlation limits among Poisson variables
correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL)

#See also Cor.PP.Limit in R package PoisNor 

#Correlation limits among binary variables
correlation.limits(n.P=0,n.B,n.C=0,lambda.vec=NULL,prop.vec,coef.mat=NULL)

#See also correlation.limits in R package BinNonNor 

#Correlation limits among continuous variables
correlation.limits(n.P=0,n.B=0,n.C,lambda.vec=NULL,prop.vec=NULL,coef.mat)

#Correlation limits among Poisson and binary variables and within themselves.
correlation.limits(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL)

#Correlation limits among Poisson and continuous variables and within themselves.
correlation.limits(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL,coef.mat)

#Correlation limits among binary and continuous variables and within themselves.
correlation.limits(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat)

#Correlation limits among Poisson, binary, and continuous variables and within themselves.
correlation.limits(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat)

n.P<-2
lambda.vec=c(-1,1)
correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL)


## End(Not run)

Computes the coefficients of Fleishman third order polynomials

Description

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

Usage

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

Arguments

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.

See Also

validation.skewness.kurtosis

Examples

## 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.C,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)

Simulates a sample of size n from a set of multivariate Poisson, binary, and continuous data

Description

This function simulates a sample of size n from a set of multivariate Poisson, binary, and continuous data with pre-specified marginals and a correlation matrix.

Usage

gen.PoisBinNonNor(n, n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, 
mean.vec=NULL, variance.vec=NULL, coef.mat = NULL, final.corr.mat)

Arguments

Value

A matrix of size n*(n.P + n.B + n.C), of which the first n.P columns are Poisson variables, the next n.B columns are binary variables, and the last n.C columns are continuous variables.

Examples

## Not run: 
n=100000
n.P<-2
n.B<-2
n.C<-2
lambda.vec<-c(2,3)
prop.vec<-c(0.3,0.5)
mean.vec<-c(0,0)
variance.vec<-c(1,1)
coef.mat=matrix(rep(c(0,1,0,0), each=2),4,2,byrow=T)
corr.mat=matrix(0.4,6,6)
diag(corr.mat)=1
final.corr.mat=overall.corr.mat(n.P,n.B,n.C,lambda.vec,prop.vec, 
coef.mat,corr.vec=NULL,corr.mat)

mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.C,lambda.vec,prop.vec, 
mean.vec,variance.vec,coef.mat,final.corr.mat)

#Check marginals
#apply(mymixdata,2,mean)
#cor(mymixdata)

n=100000
n.P<-2
n.B<-2
n.N<-2
lambda.vec<-c(2,3)
prop.vec<-c(0.3,0.5)
mean.vec=c(1,0.5)
variance.vec=c(1,0.02777778)
skewness.vec=c(2,0)
kurtosis.vec=c(6,-0.5455)
coef.mat=fleishman.coef(2,skewness.vec, kurtosis.vec)
corr.mat=matrix(0.3,6,6)
diag(corr.mat)=1
final.corr.mat=overall.corr.mat(n.P,n.B,n.N,lambda.vec,prop.vec,
coef.mat,corr.vec=NULL,corr.mat)
mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.N,lambda.vec,prop.vec,
mean.vec, variance.vec,coef.mat,final.corr.mat)

#Check marginals
#apply(mymixdata,2,mean)[4:5] 
#apply(mymixdata,2,var)[4:5]  
#cor(mymixdata)

## End(Not run)

Computes an intermediate normal correlation matrix for binary variables given the specified correlation matrix

Description

Computes an intermediate normal correlation matrix for binary variables before dichotomization given the specified correlation matrix.

Usage

intermediate.corr.BB(n.P, n.B, n.C, prop.vec, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.B*n.B.

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.

See Also

intermediate.corr.PB, intermediate.corr.BC

Examples

## Not run: 
n.P<-2
n.B<-2
n.C<-2
prop.vec=c(0.4,0.7)
corr.vec = NULL
corr.mat=matrix(c(1.0,-0.3,-0.3,-0.3,-0.3,-0.3,
-0.3,1.0,-0.3,-0.3,-0.3,-0.3,
-0.3,-0.3,1.0,0.4,0.5,0.6,
-0.3,-0.3,0.4,1.0,0.7,0.8,
-0.3,-0.3,0.5,0.7,1.0,0.9,
-0.3,-0.3,0.6,0.8,0.9,1.0),6,by=TRUE)

intmatBB=intermediate.corr.BB(n.P,n.B,n.C,prop.vec,corr.vec=NULL,corr.mat)
intmatBB

## End(Not run)

Computes intermediate correlation matrix for binary and continuous variables given the specified correlation matrix

Description

This function computes the intermediate correlation matrix for binary-continuous combinations as formulated in Demirtas et al. (2012).

Usage

intermediate.corr.BC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, 
coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.B*n.C.

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.

See Also

intermediate.corr.BB, intermediate.corr.CC

Examples

## Not run: 
n.B<-2
n.C<-4
prop.vec=c(0.4,0.7)
coef.mat=matrix(c(
 -0.31375,  0.00000,  0.10045, -0.10448,
  0.82632,  1.08574,  1.10502,  0.98085,
  0.31375,  0.00000, -0.10045,  0.10448,
  0.02271, -0.02945, -0.04001,  0.00272),4,byrow=TRUE)
corr.vec = NULL
corr.mat=matrix(c(1.0,-0.3,-0.3,-0.3,-0.3,-0.3,
-0.3,1.0,-0.3,-0.3,-0.3,-0.3,
-0.3,-0.3,1.0,0.4,0.5,0.6,
-0.3,-0.3,0.4,1.0,0.7,0.8,
-0.3,-0.3,0.5,0.7,1.0,0.9,
-0.3,-0.3,0.6,0.8,0.9,1.0),6,byrow=TRUE)

intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, 
corr.vec=NULL,corr.mat)
intmatBC

n.B<-1
n.C<-1
prop.vec=0.6
coef.mat=matrix(c(-0.31375,0.82632,0.31375,0.02271),4,1)
corr.vec=NULL
corr.mat=matrix(c(1,-0.3,-0.3,1),2,2)

intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, 
corr.vec=NULL,corr.mat)
intmatBC

## End(Not run)

Computes an intermediate correlation matrix for continuous variables given the specified correlation matrix

Description

This function computes the intermediate correlation matrix for continuous-continuous combinations as formulated in Demirtas et al. (2012).

Usage

intermediate.corr.CC(n.P, n.B, n.C, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.C*n.C.

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.

Vale, C.D. and Maurelli, V.A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.

See Also

intermediate.corr.PC, intermediate.corr.BC

Examples

## Not run: 
n.P=2
n.C=4
coef.mat=matrix(c(
 -0.31375,  0.00000,  0.10045, -0.10448,
  0.82632,  1.08574,  1.10502,  0.98085,
  0.31375,  0.00000, -0.10045,  0.10448,
  0.02271, -0.02945, -0.04001,  0.00272),4,byrow=TRUE)
corr.vec = NULL
corr.mat=matrix(c(1.0,-0.3,-0.3,-0.3,-0.3,-0.3,
-0.3,1.0,-0.3,-0.3,-0.3,-0.3,
-0.3,-0.3,1.0,0.4,0.5,0.6,
-0.3,-0.3,0.4,1.0,0.7,0.8,
-0.3,-0.3,0.5,0.7,1.0,0.9,
-0.3,-0.3,0.6,0.8,0.9,1.0),6,byrow=TRUE)

intmatCC=intermediate.corr.CC(n.P,n.B=0,n.C,coef.mat,corr.vec=NULL,corr.mat)
intmatCC

## End(Not run)

Computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-binary combinations given the specified correlation matrix.

Description

This function computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-binary combinations given the specified correlation matrix as formulated in Amatya and Demirtas (2015).

Usage

intermediate.corr.PB(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, 
coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A matrix of n.P*n.B.

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, (85)15, 3129-3139.

See Also

intermediate.corr.PP, intermediate.corr.BB

Examples

## Not run: 
n.P<-2
n.B<-1
lambda.vec<-c(2,3)
prop.vec<-c(0.3)
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)

intmatPB=intermediate.corr.PB(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL, 
corr.vec=NULL,corr.mat)
intmatPB

## End(Not run)

Computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-continuous combinations given the specified correlation matrix.

Description

This function computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-continuous combinations given the specified correlation matrix as formulated in Amatya and Demirtas (2015).

Usage

intermediate.corr.PC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, 
corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.P*n.C.

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, (85)15, 3129-3139.

See Also

intermediate.corr.PP, intermediate.corr.CC

Examples

## Not run: 
n.P=2
n.C=4
lambda.vec=c(2,3)
coef.mat=matrix(rep(c(0,1,0,0),each=4),4,byrow=TRUE)
corr.vec = NULL
corr.mat=matrix(c(1.0,-0.3,-0.3,-0.3,-0.3,-0.3,
-0.3,1.0,-0.3,-0.3,-0.3,-0.3,
-0.3,-0.3,1.0,0.4,0.5,0.6,
-0.3,-0.3,0.4,1.0,0.7,0.8,
-0.3,-0.3,0.5,0.7,1.0,0.9,
-0.3,-0.3,0.6,0.8,0.9,1.0),6,byrow=TRUE)

intmatPC=intermediate.corr.PC(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL, 
coef.mat,corr.vec=NULL,corr.mat)

intmatPC

#See also cmat.star in  R package PoisNor 
#cmat.star(no.pois=2,no.norm=4,corMat=corr.mat,lamvec=lambda.vec)

## End(Not run)

Computes an intermediate normal correlation matrix for Poisson variables given the specified correlation matrix

Description

This function computes the intermediate normal correlation matrix for Poisson-Poisson combinations before inverse cdf matching as formulated in Amatya and Demirtas (2015).

Usage

intermediate.corr.PP(n.P, n.B, n.C, lambda.vec, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.P*n.P.

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, (85)15, 3129-3139.

See Also

intermediate.corr.PB, intermediate.corr.PC

Examples

n.P<-3
lambda.vec<-c(1,2,3)
corr.mat<-matrix(c(1,0.352,0.265,0.352,1,0.121,0.265,0.121,1),n.P,n.P)
intmatPP=intermediate.corr.PP(n.P,n.B=0,n.C=0,lambda.vec,corr.vec=NULL,corr.mat)
intmatPP

## Not run: 
#See also cmat.star in  R package PoisNor 
#cmat.star(no.pois=3,no.norm=0,corMat=corr.mat,lamvec=lambda.vec)

## End(Not run)

Computes the final intermediate correlation matrix

Description

This function computes the final correlation matrix by combining pairwise intermediate correlation matrix entries for Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations. If the resulting correlation matrix is not positive definite, a nearest positive matrix will be used.

Usage

overall.corr.mat(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, 
corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size (n.P+N.B+n.C)*(n.P+N.B+n.C).

See Also

intermediate.corr.PP, intermediate.corr.BB, intermediate.corr.CC,

intermediate.corr.PB, intermediate.corr.PC, intermediate.corr.BC

Examples

## Not run: 
n.P<-1
n.B<-1
n.C<-1
lambda.vec<-c(1)
prop.vec<-c(0.3)
coef.mat<-matrix(c(0,1,0,0),4,1)
corr.vec=NULL
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)

finalmat=overall.corr.mat(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat, 
corr.vec=NULL,corr.mat)
finalmat

## End(Not run)

Validates the marginal specification of the binary variables

Description

Checks whether the marginal specification of the binary part is valid and consistent.

Usage

validation.bin(n.B, prop.vec = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

Examples

n.B<-3
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B, prop.vec)

## Not run: 
n.B<-3
validation.bin(n.B)

n.B<--3
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B, prop.vec)

n.B<-0
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B, prop.vec)

n.B<-5
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B, prop.vec)

n.B<-3
prop.vec<-c(0.25,0.5,-0.75)
validation.bin(n.B, prop.vec)

## End(Not run)

Validates the specified correlation matrix

Description

This function validates the specified correlation vector and/or matrix for appropriate dimension, symmetry, range, and positive definiteness. If both correlation matrix and correlation vector are supplied, it checks whether the matrix and vector are conformable.

Usage

validation.corr(n.P, n.B, n.C, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

See Also

correlation.limits, correlation.bound.check

Examples

n.P<-1
n.B<-1
n.C<-1
corr.vec=c(0.2,0.1,0.5)
validation.corr(n.P,n.B,n.C,corr.vec,corr.mat=NULL)

n.P<-2
n.B<-2
n.C<-2
corr.mat=matrix(0.5,6,6)
diag(corr.mat)=1
validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat)

## Not run: 
n.P<-2
n.B<-2
n.C<-1
corr.mat=matrix(0.5,6,6)
diag(corr.mat)=1
validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat)

n.P<-2
n.B<-2
n.C<-2
corr.mat=matrix(0.5,6,6)
corr.mat[1,2]=0.4
diag(corr.mat)=1
validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat)

## End(Not run)

Validates the marginal specification of the continuous variables

Description

Checks whether the marginal specification of the continuous part is valid and consistent.

Usage

validation.skewness.kurtosis(n.C, skewness.vec = NULL, kurtosis.vec = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

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.

Examples

n.C<-3
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6,8)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

## Not run: 
n.C<--1
skewness.vec=c(0)
kurtosis.vec=c(-1.2)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

n.C<-3
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6,5)
validation.skewness.kurtosis(3)

n.C<-3
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6,5)
validation.skewness.kurtosis(n.C,skewness.vec)
validation.skewness.kurtosis(n.C,kurtosis.vec)

n.C<-0
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6,8)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

n.C<-2
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6,8)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

n.C<-2
skewness.vec=c(0,2,3)
kurtosis.vec=c(-1.2,6)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

skewness.vec=c(2,3)
kurtosis.vec=c(1,5)
validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec)

## End(Not run)