# 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
[1] 0.3874747
[1] 0.3874747

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