poly_skurt_check {SimMultiCorrData} | R Documentation |
Headrick's Fifth-Order Transformation Lagrangean Constraints for Lower Boundary of Standardized Kurtosis
Description
This function gives the first-order conditions of the multi-constraint Lagrangean expression
used to find the lower kurtosis boundary for a given skewness and standardized fifth and sixth cumulants
in calc_lower_skurt
. The partial derivatives are described in Headrick (2002,
doi: 10.1016/S0167-9473(02)00072-5), but he does not provide
the actual equations. The equations used here were found with D
(see deriv
).
Here, are the Lagrangean multipliers,
are the user-specified
values of skewness, fifth cumulant, and sixth cumulant, and
are the equations for standardized kurtosis, variance,
fifth cumulant, and sixth cumulant expressed in terms of the constants. This function would not ordinarily be called by the user.
Usage
poly_skurt_check(c, a)
Arguments
c |
a vector of constants c1, ..., c5, lambda1, ..., lambda4 |
a |
a vector of skew, fifth standardized cumulant, sixth standardized cumulant |
Value
A list with components:
If the suppled values for c
and a
satisfy the Lagrangean expression, it will return 0 for each component.
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)
Headrick TC (2004). On Polynomial Transformations for Simulating Multivariate Nonnormal Distributions. Journal of Modern Applied Statistical Methods, 3(1), 65-71. doi: 10.22237/jmasm/1083370080.
Headrick TC, Kowalchuk RK (2007). The Power Method Transformation: Its Probability Density Function, Distribution Function, and Its Further Use for Fitting Data. Journal of Statistical Computation and Simulation, 77, 229-249. doi: 10.1080/10629360600605065.
Headrick TC, Sheng Y, & Hodis FA (2007). Numerical Computing and Graphics for the Power Method Transformation Using Mathematica. Journal of Statistical Software, 19(3), 1 - 17. doi: 10.18637/jss.v019.i03.