U1.Gumbel {Copula.surv}R Documentation

Estimation of an association parameter via the unweighted estimator

Description

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

Usage

U1.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

theta

association parameter

tau

Kendall's tau (=theta/(theta+2))

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(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
y.obs=c(2,1,4,5,6,8,3,7,10,9,11,12,13,14,15)
dx=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
dy=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
U1.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
U1.Gumbel(x.obs,y.obs,dx,dy)

[Package Copula.surv version 1.1 Index]