# simu.Clayton: Simulating data from the Clayton copula In Copula.surv: Association Analysis of Bivariate Survival Data Based on Copulas

## 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

 `1` ```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

 ```1 2 3 4 5 6``` ```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") ```

### Example output  ```true_Kendall_tau
0.3333333
 0.3874747
 0.3874747
```

Copula.surv documentation built on Jan. 13, 2021, 8:51 a.m.