U1.Clayton | R Documentation |
Estimate the association parameter of the Clayton copula using bivariate survival data. The estimator was derived by Clayton (1978) and reformulated by Emura, Lin and Wang (2010).
U1.Clayton(x.obs,y.obs,dx,dy,lower=0.001,upper=50,U.plot=TRUE)
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) |
Details are seen from the references.
theta |
association parameter |
tau |
Kendall's tau (=theta/(theta+2)) |
Takeshi Emura
Clayton DG (1978). A model for association in bivariate life tables and its application to epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65: 141-51.
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
n=200 theta_true=2 ## association parameter ## r1_true=1 ## hazard for X r2_true=1 ## hazard for Y set.seed(1) V1=runif(n) V2=runif(n) X=-1/r1_true*log(1-V1) W=(1-V1)^(-theta_true) Y=1/theta_true/r2_true*log( 1-W+W*(1-V2)^(-theta_true/(theta_true+1)) ) C=runif(n,min=0,max=5) x.obs=pmin(X,C) y.obs=pmin(Y,C) dx=X<=C dy=Y<=C U1.Clayton(x.obs,y.obs,dx,dy)
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