Test.Gumbel {Copula.surv} R Documentation

## A goodness-of-fit test for the Gumbel copula

### Description

Perform a goodness-of-fit test for the Gumbel copula based on Emura, Lin and Wang (2010).

### Usage

```Test.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) and U_2(theta)

### Details

See the references.

### Value

 `alpha1` association parameter by the pseudo-likelihood estimator `alpha2` association parameter by the unweighted estimator `Stat` log(alpha1)-log(alpha2) `Z` Z-value of the goodness-of-fit for the Gumbel copula `P` P-value of the goodness-of-fit for the Gumbel copula

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)
Test.Gumbel(x.obs,y.obs,dx,dy)

n=20
set.seed(1)
Dat=simu.Clayton(n=n,alpha=2)
C=runif(n,min=0,max=5)
x.obs=pmin(Dat[,"X"],C)
y.obs=pmin(Dat[,"Y"],C)
dx=Dat[,"X"]<=C
dy=Dat[,"Y"]<=C
Test.Gumbel(x.obs,y.obs,dx,dy)
```

[Package Copula.surv version 1.1 Index]