This function computes the theoretical Blomqvist's beta value of a bivariate copula for given parameter values.
BiCopPar2Beta(family, par, par2 = 0, obj = NULL, check.pars = TRUE)Theoretical value of Blomqvist's beta corresponding to the bivariate
copula family and parameter(s) par, par2.
integer; single number or vector of size n; defines the
bivariate copula family:
0 = independence copula
2 = Student t copula (t-copula)
1 = Gaussian 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)
Note that the Student's t-copula is not allowed since the CDF of the t-copula
is not implemented (see BiCopCDF()).
numeric; single number or vector of size n; copula
parameter.
numeric; single number or vector of size n; second
parameter for the two parameter BB1, BB6, BB7, BB8, Tawn type 1 and type 2
copulas (default: par2 = 0).
BiCop object containing the family and parameter
specification.
logical; default is TRUE; if FALSE, checks
for family/parameter-consistency are omitted (should only be used with
care).
Ulf Schepsmeier
If the family and parameter specification is stored in a BiCop()
object obj, the alternative version
BiCopPar2Beta(obj)can be used.
Blomqvist, N. (1950). On a measure of dependence between two random variables. The Annals of Mathematical Statistics, 21(4), 593-600.
Nelsen, R. (2006). An introduction to copulas. Springer
## Example 1: Gaussian copula
BiCopPar2Beta(family = 1, par = 0.7)
BiCop(1, 0.7)$beta # alternative
## Example 2: Clayton copula
BiCopPar2Beta(family = 3, par = 2)
## Example 3: different copula families
BiCopPar2Beta(family = c(3,4,6), par = 2:4)
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