tau_copula {CopulaCenR} | R Documentation |
Calculate Kendall's tau
Description
To obtain Kendall's tau from copula parameter(s)
Usage
tau_copula(eta, copula)
Arguments
eta |
copula parameter(s);
if |
copula |
specify the type of copula model |
Details
The supported copula models are "Clayton"
, "Gumbel"
, "Frank"
,
"AMH"
, "Joe"
and "Copula2"
.
The "Copula2"
model is a two-parameter copula model that incorporates
Clayton
and Gumbel
as special cases.
The Kendall's formulas are list below:
The Clayton copula Kendall's .
The Gumbel copula Kendall's .
The Frank copula Kendall's ,
in which
.
The AMH copula Kendall's .
The Joe copula Kendall's .
The Two-parameter copula (Copula2
) Kendall's .
Value
Kendall's
Source
Ali MM, Mikhail NN, Haq MS (1978).
A Class of Bivariate Distributions Including the Bi- variate Logistic.
Journal of Multivariate Analysis doi:10.1016/0047-259X(78)90063-5.
Clayton DG (1978).
A Model for Association in Bivariate Life Tables and Application in
Epidemiological Studies of Familial Tendency in Chronic Disease Incidence.
Biometrika doi:10.2307/2335289.
Gumbel EJ (1960).
Bivariate Exponential Distributions.
Journal of the American Statistical Association
doi:10.2307/2281591.
Joe H (1993).
Parametric Families of Multivariate Distributions with Given Margins.
Journal of Multivariate Analysis
doi:10.1006/jmva.1993.1061.
Joe H (1997).
Multivariate Models and Dependence Concepts.
Chapman & Hall, London.
Frank MJ (1979).
On the Simultaneous Associativity of
and
.
Aequationes Mathematicae.
Examples
# fit a Copula2-Semiparametric model
data(AREDS)
copula2_sp <- ic_spTran_copula(data = AREDS, copula = "Copula2",
l = 0, u = 15, m = 3, r = 3,
var_list = c("ENROLLAGE","rs2284665","SevScaleBL"))
tau_copula(eta = as.numeric(coef(copula2_sp)[c("alpha","kappa")]),
copula = "Copula2")