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

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

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]