simu.Clayton {Copula.surv} R Documentation

## Simulating data from the Clayton copula

### Description

n pairs of (U,V) are generated from the Clayton copula. n paris of (X,Y) are generated from the corresponding bivariate survival model with the Weibull marginal distributions. The default parameters (scale1=scale2=shape1=shape2=1) give the unit exponential distributions.

### Usage

```simu.Clayton(n,alpha,scale1=1,scale2=1,shape1=1,shape2=1)
```

### Arguments

 `n` sample size `alpha` association parameter `scale1` scale parameter for X `scale2` scale parameter for Y `shape1` shape parameter for X `shape2` shape parameter for Y

### Details

See Section 2.6 of Emura et al.(2019) for copulas and bivariate survival times.

### Value

 `U` uniformly distributed on (0,1) `V` uniformly distributed on (0,1) `X` Weibull distributed (scale1, shape1) `Y` Weibull distributed (scale2, shape2)

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

Emura T, Matsui S, Rondeau V (2019), Survival Analysis with Correlated Endpoints, Joint Frailty-Copula Models, JSS Research Series in Statistics, Springer

### Examples

```n=100
Dat=simu.Clayton(n=n,alpha=1,scale1=1,scale2=2,shape1=0.5,shape2=2)
plot(Dat[,"U"],Dat[,"V"])
cor(Dat[,"U"],Dat[,"V"],method="kendall")
plot(Dat[,"X"],Dat[,"Y"])
cor(Dat[,"X"],Dat[,"Y"],method="kendall")
```

[Package Copula.surv version 1.1 Index]