BiCopCDF {VineCopula} | R Documentation |
Distribution Function of a Bivariate Copula
Description
This function evaluates the cumulative distribution function (CDF) of a
given parametric bivariate copula.
Usage
BiCopCDF(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)
Arguments
u1 , u2 |
numeric vectors of equal length with values in [0,1] .
|
family |
integer; single number or vector of size length(u1) ;
defines the bivariate copula family:
0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
7 = BB1 copula
8 = BB6 copula
9 = BB7 copula
10 = BB8 copula
13 = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”)
16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1”)
18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `19` = rotated BB7 copula (180 degrees; survival BB7”)
20 = rotated BB8 copula (180 degrees; “survival BB8”)
23 = rotated Clayton copula (90 degrees)
'24' = rotated Gumbel copula (90 degrees)
'26' = rotated Joe copula (90 degrees)
'27' = rotated BB1 copula (90 degrees)
'28' = rotated BB6 copula (90 degrees)
'29' = rotated BB7 copula (90 degrees)
'30' = rotated BB8 copula (90 degrees)
'33' = rotated Clayton copula (270 degrees)
'34' = rotated Gumbel copula (270 degrees)
'36' = rotated Joe copula (270 degrees)
'37' = rotated BB1 copula (270 degrees)
'38' = rotated BB6 copula (270 degrees)
'39' = rotated BB7 copula (270 degrees)
'40' = rotated BB8 copula (270 degrees)
'104' = Tawn type 1 copula
'114' = rotated Tawn type 1 copula (180 degrees)
'124' = rotated Tawn type 1 copula (90 degrees)
'134' = rotated Tawn type 1 copula (270 degrees)
'204' = Tawn type 2 copula
'214' = rotated Tawn type 2 copula (180 degrees)
'224' = rotated Tawn type 2 copula (90 degrees)
'234' = rotated Tawn type 2 copula (270 degrees)
|
par |
numeric; single number or vector of size length(u1) ;
copula parameter.
|
par2 |
numeric; single number or vector of size length(u1) ;
second parameter for bivariate copulas with two parameters (BB1, BB6, BB7,
BB8, Tawn type 1 and type 2; default: par2 = 0 ).
|
obj |
BiCop object containing the family and parameter
specification.
|
check.pars |
logical; default is TRUE ; if FALSE , checks
for family/parameter-consistency are omitted (should only be used with
care).
|
Details
If the family and parameter specification is stored in a BiCop()
object obj
, the alternative version
BiCopCDF(u1, u2, obj)
can be used.
Value
A numeric vector of the bivariate copula distribution function
Note
The calculation of the cumulative distribution function (CDF) of the
Student's t copula (family = 2
) is only approximate. For numerical
reasons, the degree of freedom parameter (par2
) is rounded to an
integer before calculation of the CDF.
Author(s)
Eike Brechmann
See Also
BiCopPDF()
,
BiCopHfunc()
,
BiCopSim()
,
BiCop()
Examples
## simulate from a bivariate Clayton copula
set.seed(123)
cop <- BiCop(family = 3, par = 3.4)
simdata <- BiCopSim(300, cop)
## evaluate the distribution function of the bivariate Clayton copula
u1 <- simdata[,1]
u2 <- simdata[,2]
BiCopCDF(u1, u2, cop)
## select a bivariate copula for the simulated data
cop <- BiCopSelect(u1, u2)
summary(cop)
## and evaluate its CDF
BiCopCDF(u1, u2, cop)
[Package
VineCopula version 2.5.0
Index]