CvM.GFGM.BurrIII {GFGM.copula}

The Cramer-von Mises type statistics under the generalized FGM copula

Description

Compute the Cramer-von Mises type statistics under the generalized FGM copula.

Usage

CvM.GFGM.BurrIII(
  t.event,
  event1,
  event2,
  Alpha,
  Beta,
  Gamma,
  g1,
  g2,
  p,
  q,
  theta,
  eta = 0,
  Sdist.plot = TRUE
)

Arguments

t.event

Vector of the observed failure times.

event1

Vector of the indicators for the failure cause 1.

event2

Vector of the indicators for the failure cause 2.

Alpha

Positive shape parameter for the Burr III margin (failure cause 1).

Beta

Positive shape parameter for the Burr III margin (failure cause 2).

Gamma

Common positive shape parameter for the Burr III margins.

g1

Splines coefficients for the failure cause 1.

g2

Splines coefficients for the failure cause 2.

p

Copula parameter that greater than or equal to 1.

q

Copula parameter that greater than 1 (integer).

theta

Copula parameter with restricted range.

eta

Location parameter with default value 0.

Sdist.plot

Plot sub-distribution functions if TRUE.

Details

The copula parameter q is restricted to be a integer due to the binominal theorem. The admissible range of theta is given in Dependence.GFGM.

Value

S.overall

Cramer-von Mises type statistic based on parametric and non-parametric estimators of sub-distribution functions for testing overall model.

S.GFGM

Cramer-von Mises type statistic based on semi-parametric and non-parametric estimators of sub-distribution functions for testing the generalized FGM copula.

References

Shih J-H, Emura T (2018) Likelihood-based inference for bivariate latent failure time models with competing risks udner the generalized FGM copula, Computational Statistics, 33:1293-1323.

See Also

Dependence.GFGM, MLE.GFGM.BurrIII, MLE.GFGM.spline

Examples

con   = c(16,224,16,80,128,168,144,176,176,568,392,576,128,56,112,160,384,600,40,416,
          408,384,256,246,184,440,64,104,168,408,304,16,72,8,88,160,48,168,80,512,
          208,194,136,224,32,504,40,120,320,48,256,216,168,184,144,224,488,304,40,160,
          488,120,208,32,112,288,336,256,40,296,60,208,440,104,528,384,264,360,80,96,
          360,232,40,112,120,32,56,280,104,168,56,72,64,40,480,152,48,56,328,192,
          168,168,114,280,128,416,392,160,144,208,96,536,400,80,40,112,160,104,224,336,
          616,224,40,32,192,126,392,288,248,120,328,464,448,616,168,112,448,296,328,56,
          80,72,56,608,144,408,16,560,144,612,80,16,424,264,256,528,56,256,112,544,
          552,72,184,240,128,40,600,96,24,184,272,152,328,480,96,296,592,400,8,280,
          72,168,40,152,488,480,40,576,392,552,112,288,168,352,160,272,320,80,296,248,
          184,264,96,224,592,176,256,344,360,184,152,208,160,176,72,584,144,176)
uncon = c(368,136,512,136,472,96,144,112,104,104,344,246,72,80,312,24,128,304,16,320,
          560,168,120,616,24,176,16,24,32,232,32,112,56,184,40,256,160,456,48,24,
          200,72,168,288,112,80,584,368,272,208,144,208,114,480,114,392,120,48,104,272,
          64,112,96,64,360,136,168,176,256,112,104,272,320,8,440,224,280,8,56,216,
          120,256,104,104,8,304,240,88,248,472,304,88,200,392,168,72,40,88,176,216,
          152,184,400,424,88,152,184)
cen   = rep(630,44)

t.event = c(con,uncon,cen)
event1  = c(rep(1,length(con)),rep(0,length(uncon)),rep(0,length(cen)))
event2  = c(rep(0,length(con)),rep(1,length(uncon)),rep(0,length(cen)))

library(GFGM.copula)
#res.BurrIII = MLE.GFGM.BurrIII(t.event,event1,event2,5000,3,2,0.75,eta = -71)
#Alpha = res.BurrIII$Alpha[1]
#Beta = res.BurrIII$Beta[1]
#Gamma = res.BurrIII$Gamma[1]
#res.spline = MLE.GFGM.spline(t.event,event1,event2,3,2,0.75)
#g1 = res.spline$g1
#g2 = res.spline$g2
#CvM.GFGM.BurrIII(t.event,event1,event2,Alpha,Beta,Gamma,g1,g2,3,2,0.75,eta = -71)