MLE.GFGM.BurrIII: Maximum likelihood estimation for bivariate dependent...

In GFGM.copula: Generalized Farlie-Gumbel-Morgenstern Copula

Description

Maximum likelihood estimation for bivariate dependent competing risks data under the generalized FGM copula with the Burr III margins.

Usage

MLE.GFGM.BurrIII(
  t.event,
  event1,
  event2,
  D,
  p,
  q,
  theta,
  eta = 0,
  Gamma.0 = 1,
  epsilon.0 = 1e-05,
  epsilon.1 = 1e-10,
  epsilon.2 = 1e-300,
  r.1 = 1,
  r.2 = 1,
  r.3 = 1
)

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.
D	Positive tunning parameter in the NR algorithm.
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.
Gamma.0	Initial guess for the common shape parameter gamma with default value 1.
epsilon.0	Positive tunning parameter in the NR algorithm with default value 1e-5.
epsilon.1	Positive tunning parameter in the NR algorithm with default value 1e-10.
epsilon.2	Positive tunning parameter in the NR algorithm with default value 1e-300.
r.1	Positive tunning parameter in the NR algorithm with default value 1.
r.2	Positive tunning parameter in the NR algorithm with default value 1.
r.3	Positive tunning parameter in the NR algorithm with default value 1.

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

n	Sample size.
count	Iteration number.
random	Randomization number.
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 shape parameter for the Burr III margins.
MeanX	Mean lifetime due to failure cause 1.
MeanY	Mean lifetime due to failure cause 2.
logL	Log-likelihood value under the fitted model.

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.

Shih J-H, Emura T (2019) Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula, Statistical Papers, 60:1101-1118.

See Also

Dependence.GFGM

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)
MLE.GFGM.BurrIII(t.event,event1,event2,5000,3,2,0.75,eta = -71)

GFGM.copula documentation built on Dec. 11, 2019, 5:07 p.m.