simu.Gumbel {Copula.surv}

Simulating data from the Gumbel copula

Description

n pairs of (U,V) are generated from the Gumbel 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.Gumbel(n,alpha,scale1=1,scale2=1,shape1=1,shape2=1,Print=FALSE)

Arguments

n

sample size

alpha

association (copula) parameter

scale1

scale parameter for X

scale2

scale parameter for Y

shape1

shape parameter for X

shape2

shape parameter for Y

Print

print Kendall's tau and means of X and Y if "TRUE"

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)

Author(s)

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.Gumbel(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")