U2.Gumbel {Copula.surv}R Documentation

Estimation of an association parameter via the pseudo-likelihood

Description

Estimate the association parameter (alpha) of the Gumbel copula using bivariate survival data. The estimator was derived by Emura, Lin and Wang (2010).

Usage

U2.Gumbel(x.obs,y.obs,dx,dy,lower=0.1,upper=50,U.plot=TRUE)

Arguments

x.obs

censored times for X

y.obs

censored times for Y

dx

censoring indicators for X

dy

censoring indicators for Y

lower

lower bound for the association parameter

upper

upper bound for the association parameter

U.plot

if TRUE, draw the plot of U_1(theta)

Details

Details are seen from the references.

Value

alpha

association parameter

tau

Kendall's tau (=alpha/(alpha+1))

Author(s)

Takeshi Emura

References

Emura T, Lin CW, Wang W (2010) A goodness-of-fit test for Archimedean copula models in the presence of right censoring, Compt Stat Data Anal 54: 3033-43

Examples

x.obs=c(1,2,3,4,5)
y.obs=c(2,1,4,5,6)
dx=c(1,1,1,1,1)
dy=c(1,1,1,1,1)
U2.Gumbel(x.obs,y.obs,dx,dy)

n=100
Dat=simu.Clayton(n=n,scale1=1,scale2=2,shape1=0.5,shape2=2,alpha=1)
x.obs=Dat[,"X"]
y.obs=Dat[,"Y"]
dx=dy=rep(1,n) ## uncensored data
U2.Gumbel(x.obs,y.obs,dx,dy)

[Package Copula.surv version 1.1 Index]