ipsA: Bivariate Archimedean copula based on integrated positive...

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Bivariate Archimedean copula based on integrated positive stable Laplace transform

Usage

pipsA(u,v,cpar)
dipsA(u,v,cpar)
pcondipsA(v,u,cpar)  # C_{2|1}(v|u;cpar)
qcondipsA(p,u,cpar)  # C_{2|1}^{-1}(p|u;cpar)
ripsA(n,cpar)
logdipsA(u,v,cpar)
ipsA.cpar2tau(cpar)
ipsA.tau2cpar(tau,mxiter=20,eps=1e-06, cparstart=0, iprint=F)

Arguments

u	value in interval 0,1; could be a vector
v	value in interval 0,1; could be a vector
p	quantile in interval 0,1; could be a vector
cpar	parameter: could be scalar or vector (positive-valued)
n	sample size for ripsA, positive integer
tau	tau in interval (-1,1), could be a vector
mxiter	maximum number of Newton-Raphson iterations
eps	tolerance for convergence of Newton-Raphson iterations
cparstart	starting point for Newton-Raphson iterations
iprint	print flag for Newton-Raphson iterations

Details

For the reflected copula, the functions are pipsAr, dipsAr, pcondipsAr, qcondipsAr, logdipsAr.

Value

cdf, pdf, conditional cdf, conditional quantile value(s) for pipsA, dipsA, pcondipsA, qcondipsA respectively;

log density for logdipsA;

random pairs for ripsA;

Kendall's tau for psA.cpar2tau;

copula parameter for ipsA.tau2cpar or parameter value for a given Kendall's tau.

References

Joe H and Ma C (2000). Multivariate survival functions with a min-stable property. Journal of Multivariate Analysis, 75, 13-35.

Examples

u=seq(.1,.6,.1)
v=seq(.4,.9,.1)
cpar=.6
pp=pcondipsA(v,u,cpar)
vv=qcondipsA(pp,u,cpar)
print(pp)
print(vv)
tau=ipsA.cpar2tau(cpar)
print(tau)
tauv=seq(-.9,.9,.1)
cpar=ipsA.tau2cpar(tauv)
print(cpar)
set.seed(123)
udata=ripsA(500,cpar=cpar[15]) # tau=0.5
print(taucor(udata[,1],udata[,2]))
print(cor(udata,method="kendall"))

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.