copula {acopula} | R Documentation |
Produce a list containing CDF and/or PDF of an copula with parameters bounds.
copula(name,...) copFGM(...) copGumbel(...) copNormal(dim=2,...) copPlackett(...) copProduct(...)
name |
character. Code name for copula, identical with the part after |
dim |
integer. Copula dimension. |
... |
named arguments. Items of the copula definition list to be redefined. Argument names must NOT be cropped. |
Currently implemented copula families:
family | CDF C(t)= | par.range | special cases |
Farlie-Gumbel-Morgenstern | prod(t)*(p*prod(1-t)+1) | [-1,1] | 0(Π) |
Gumbel-Hougaard | exp(-sum((-log(t))^p)^(1/p)) | [1,Inf] | 1(Π),Inf(M) |
normal | Φ_P(Φ^-1(t_1),...) | ]-1,1[ | -1(W),0(Π),1(M) |
Plackett | (A-sqrt(A^2-4*prod(t)*p*(p-1)))/(2*(p-1)); A=1+(p-1)*sum(t) | [0,Inf] | 0(W),1(Π),Inf(M) |
product | prod(t) | Π | |
where Φ^-1 is quantile function of standard normal and Φ_P is CDF of multivariate normal distribution with correlation matrix P containing copula parameters.
parameters |
numeric vector to be used whenever parameters of copula are not supplied to procedure that use it, or as starting values in estimation. |
pcopula,dcopula |
function of two arguments. The first is vector of copula arguments, the another is vector of parameters. |
rcopula |
function of two arguments. The first is copula dimension or length of random sample (normal copula), the another is vector of parameters. |
kendall,spearman |
list. Correlation coefficient as function of copula parameter ( |
lower,upper |
numeric. Parameters boundary. |
id |
character. Identification of copula family. |
Tomas Bacigal
Nelsen, R. B. (2006): An introduction to copulas. Springer.
## the following gives the same definition list copFGM() copula("FGM") ## any list item can be modified upon function call copPlackett(parameters=2.2,upper=10)