| Usage: |
F = VaRcopula(uv,theta,mode,cop)
|
| Input: |
| uv | n x 2 matrix of coordinates
|
| theta | scalar, the parameter of the function
|
| mode | integer,
mode=-1: computes (dG_theta,u/du)(v)^(-1)
mode=0: computes the copula cop_theta(u,v)
mode=1,2,3: computes the first numeric derivative of
copula cop for the 1st (2nd,3rd) parameter
mode=4,5,6: computes the second numeric derivative of
copula cop for the 1st (2nd,3rd) parameter
mode=7: returns initial theta for fitting the copula cop
by newton in F
mode=8: returns minimum theta for copula cop
mode=9: returns maximum theta for copula cop
mode>9: computes derivative with respect to more than one variable,
e.g., mode=xyz where x=1, y=2, z=3 => mode=123
computes d^3Gumbel/(dparam1*dparam2*dparam3)
|
| cop | scalar, integer between 1 and 22, selects the copula.
Numbering conforms to the last digit in the table on p.94
from R. B. Nelsen, An Introduction to Copulas,
cop=1 - Pareto-Clayton,
cop=4 - Gumbel-Hougaard,
cop=5 - Frank.
|
| Output: |
| F | scalar for modes 7,8,9, (n x 1) vector otherwise; its contents
depends on the input parameter mode |