GFGM.copula (version 1.0.4)

Sdist.GFGM.BurrIII: Sub-distribution functions under the generalized FGM copula with the Burr III margins

Description

Sub-distribution functions under the generalized FGM copula with the Burr III margins.

Usage

Sdist.GFGM.BurrIII(time, Alpha, Beta, Gamma, p, q, theta, eta = 0)

Arguments

time

Vector of times.

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.

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.

Value

time

Failure times

Sdist.1

Probability of an object fails due to the failure cause 1.

Sdist.2

Probability of an object fails due to the failure cause 2.

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.

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

MLE.GFGM.BurrIII, Dependence.GFGM

Examples

# NOT RUN {
library(GFGM.copula)
Sdist.GFGM.BurrIII(c(1:5),1,1,1,3,2,0.75,eta = 1)
# }