intercor.NN {PoisNonNor} | R Documentation |
Computes the subset of the intermediate correlation matrix that is pertinent to the continuous pairs
Description
This function computes the submatrix of the intermediate correlation matrix of the multivariate normal distribution. It is relevant to the continuous part of the data.
Usage
intercor.NN(pmat, cmat)
Arguments
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
cmat |
a n2xn2 matrix of specified correlations for the continuous part. |
Details
Fleishman polynomials is a method to generate real-life non-normal distributions of variables by using their first four moments. It is based on the polynomial transformation, Y = a + bZ + cZ^2 + dZ^3
, where Z follows a standard normal distribution and Y is standardized (zero mean and unit variance).
Normal-Normal correlation for a given continuous pair can be calculated by solving the following equation.
r_{Y_1Y_2} = r_{Z_1Z_2}(b_1b_2+3b_1d_2+3d_1b_2+9d_1d_2) + r_{Z_1Z_2}^2(2c_1c_2)+r_{Z_1Z_2}^3(6d_1d_2)
Value
Returns an intermediate matrix of size n2xn2
References
Yahav, I. and Shmueli, G. (2012). On generating multivariate poisson data in management science applications. Applied Stochastic Models in Business and Industry, 28(1), 91-102.
Examples
## Not run:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
cmat = matrix(c(
1.000, 0.100, 0.354,
0.100, 1.000, 0.386,
0.354, 0.386, 1.000),nrow=3,byrow=TRUE)
intercor.NN(pmat,cmat)
## End(Not run)