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))

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]