Headrick.dist {SimMultiCorrData}

Examples of Constants Calculated by Headrick's Fifth-Order Polynomial Transformation

Description

Selected symmetrical and asymmetrical theoretical densities with their associated values of skewness (gamma1), standardized kurtosis (gamma2), and standardized fifth (gamma3) and sixth (gamma4) cumulants. Constants were calculated by Headrick using his fifth-order polynomial transformation and given in his Table 1 (2002, p. 691-2, doi: 10.1016/S0167-9473(02)00072-5). Note that the standardized cumulants for the Gamma(10, 10) distribution do not arise from using \alpha = 10,\ \beta = 10. Therefore, either there is a typo in the table or Headrick used a different parameterization.

Usage

data(Headrick.dist)

Format

An object of class "data.frame"; Colnames are distribution names; rownames are standardized cumulant names followed by c0, ..., c5.

References

Headrick TC (2002). Fast Fifth-order Polynomial Transforms for Generating Univariate and Multivariate Non-normal Distributions. Computational Statistics & Data Analysis, 40(4):685-711. doi: 10.1016/S0167-9473(02)00072-5. (ScienceDirect)

Examples

z <- rnorm(10000)
g <- Headrick.dist$Gamma_a10b10[-c(1:4)]
gamma_a10b10 <- g[1] + g[2] * z + g[3] * z^2 + g[4] * z^3 + g[5] * z^4 +
                g[6] * z^5
summary(gamma_a10b10)