generator {acopula} R Documentation

## Generator of Archimedean copula

### Description

Produce a list containing generator of specified Archimedean family, its inverse and derivatives with parameters bounds.

### Usage

generator(name,...)

genAMH(...)
genClayton(...)
genFrank(...)
genGumbel(...)
genJoe(...)
genLog(...)

### Arguments

 name character; code name for generator, identical with the part after 'gen' ... named arguments; items of the generator definition list to be redefined

### Details

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

### Value

 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 (coef), its inverse (icoef) and range (bounds). Available only for 1-parameter families. lower,upper numeric; parameters boundary id character; identification of generator family

Tomas Bacigal

### References

Nelsen, R. B.: An introduction to copulas. Springer (2006).