generator {acopula} | R Documentation |
Produce a list containing generator of specified Archimedean family, its inverse and derivatives with parameters bounds.
generator(name,...) genAMH(...) genClayton(...) genFrank(...) genGumbel(...) genJoe(...) genLog(...)
name |
character; code name for generator, identical with the part after 'gen' |
... |
named arguments; items of the generator definition list to be redefined |
Currently implemented families of Archimedean copula generator:
family | generator φ(t)= | par.range | Archimed.case |
Ali-Mikhail-Haq | log([1-(1-t)p]/t) | [-1,1[ | -1(Π) |
Clayton | t^(-p) - 1 | [0,Inf] | 0(Π),Inf(M) |
Frank | -log[(exp(-p t)-1)/(exp(-p)-1)] | [-Inf,Inf] | -Inf(W),0(Π),Inf(M) |
Gumbel-Hougaard | (-log(t))^p | [1,Inf] | 1(Π),Inf(M) |
Joe | -log(1-(1-t)^p) | [1,Inf] | 1(Π),Inf(M) |
Log | -log(t) | Π | |
parameters |
numeric vector to be used whenever parameters of generator are not supplied to procedure that use it, or as starting values in estimation. |
gen |
function of two arguments. The first is generator argument, the another is genereator parameters. |
gen.der |
function. Generator first derivative. |
gen.der2 |
function. Generator second derivative. |
gen.inv |
function. Generator inverse. |
gen.inv.der |
function. First derivative of generator inverse. |
gen.inv.der2 |
function. second derivative of generator inverse. |
kendall,spearman |
list. Correlation coefficient as function of copula parameter ( |
lower,upper |
numeric; parameters boundary |
id |
character; identification of generator family |
Tomas Bacigal
Nelsen, R. B.: An introduction to copulas. Springer (2006).
## the following gives the same definition list genGumbel() generator("Gumbel") ## any list item can be modified upon function call genGumbel(parameters=2.2,upper=10)