Sdist.GFGM.spline {GFGM.copula}

Sub-distribution functions under the generalized FGM copula with the marginal distributions approximated by splines

Description

Sub-distribution functions under the generalized FGM copula with the marginal distributions approximated by splines.

Usage

Sdist.GFGM.spline(time, g1, g2, tmin, tmax, p, q, theta)

Arguments

time

Vector of times.

g1

Splines coefficients for the failure cause 1.

g2

Splines coefficients for the failure cause 2.

tmin

Lower bound of times.

tmax

upper bound of times.

p

Copula parameter that greater than or equal to 1.

q

Copula parameter that greater than 1 (integer).

theta

Copula parameter with restricted range.

Details

The splines coefficients g1 and g2 are usually computed by MLE.GFGM.spline. 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

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.

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.spline, Dependence.GFGM

Examples

library(GFGM.copula)
Sdist.GFGM.spline(seq(1,5,1),rep(0.1,5),rep(0.1,5),1,5,3,2,0.75)