| MLE.Frank.Pareto {Bivariate.Pareto} | R Documentation |
Maximum likelihood estimation for bivariate dependent competing risks data under the Frank copula with the Pareto margins and fixed \theta
Description
Maximum likelihood estimation for bivariate dependent competing risks data under the Frank copula with the Pareto margins and fixed \theta.
Usage
MLE.Frank.Pareto(
t.event,
event1,
event2,
Theta,
Alpha1.0 = 1,
Alpha2.0 = 1,
Gamma1.0 = 1,
Gamma2.0 = 1,
epsilon = 1e-05,
d = exp(10),
r.1 = 6,
r.2 = 6,
r.3 = 6,
r.4 = 6
)
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. |
Theta |
Copula parameter |
Alpha1.0 |
Initial guess for the scale parameter |
Alpha2.0 |
Initial guess for the scale parameter |
Gamma1.0 |
Initial guess for the shape parameter |
Gamma2.0 |
Initial guess for the shape parameter |
epsilon |
Positive tunning parameter in the NR algorithm with default value |
d |
Positive tunning parameter in the NR algorithm with default value |
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. |
r.4 |
Positive tunning parameter in the NR algorithm with default value 1. |
Value
n |
Sample size. |
count |
Iteration number. |
random |
Randomization number. |
Alpha1 |
Positive scale parameter for the Pareto margin (failure cause 1). |
Alpha2 |
Positive scale parameter for the Pareto margin (failure cause 2). |
Gamma1 |
Positive shape parameter for the Pareto margin (failure cause 1). |
Gamma2 |
Positive shape parameter for the Pareto margin (failure cause 2). |
MedX |
Median lifetime due to failure cause 1. |
MedY |
Median lifetime due to failure cause 2. |
MeanX |
Mean lifetime due to failure cause 1. |
MeanY |
Mean lifetime due to failure cause 2. |
logL |
Log-likelihood value under the fitted model. |
AIC |
AIC value under the fitted model. |
BIC |
BIC value under the fitted model. |
References
Shih J-H, Lee W, Sun L-H, Emura T (2018), Fitting competing risks data to bivariate Pareto models, Communications in Statistics - Theory and Methods, doi: 10.1080/03610926.2018.1425450.
Examples
t.event = c(72,40,20,65,24,46,62,61,60,60,59,59,49,20, 3,58,29,26,52,20,
51,51,31,42,38,69,39,33, 8,13,33, 9,21,66, 5,27, 2,20,19,60,
32,53,53,43,21,74,72,14,33, 8,10,51, 7,33, 3,43,37, 5, 6, 2,
5,64, 1,21,16,21,12,75,74,54,73,36,59, 6,58,16,19,39,26,60,
43, 7, 9,67,62,17,25, 0, 5,34,59,31,58,30,57, 5,55,55,52, 0,
51,17,70,74,74,20, 2, 8,27,23, 1,52,51, 6, 0,26,65,26, 6, 6,
68,33,67,23, 6,11, 6,57,57,29, 9,53,51, 8, 0,21,27,22,12,68,
21,68, 0, 2,14,18, 5,60,40,51,50,46,65, 9,21,27,54,52,75,30,
70,14, 0,42,12,40, 2,12,53,11,18,13,45, 8,28,67,67,24,64,26,
57,32,42,20,71,54,64,51, 1, 2, 0,54,69,68,67,66,64,63,35,62,
7,35,24,57, 1, 4,74, 0,51,36,16,32,68,17,66,65,19,41,28, 0,
46,63,60,59,46,63, 8,74,18,33,12, 1,66,28,30,57,50,39,40,24,
6,30,58,68,24,33,65, 2,64,19,15,10,12,53,51, 1,40,40,66, 2,
21,35,29,54,37,10,29,71,12,13,27,66,28,31,12, 9,21,19,51,71,
76,46,47,75,75,49,75,75,31,69,74,25,72,28,36, 8,71,60,14,22,
67,62,68,68,27,68,68,67,67, 3,49,12,30,67, 5,65,24,66,36,66,
40,13,40, 0,14,45,64,13,24,15,26, 5,63,35,61,61,50,57,21,26,
11,59,42,27,50,57,57, 0, 1,54,53,23, 8,51,27,52,52,52,45,48,
18, 2, 2,35,75,75, 9,39, 0,26,17,43,53,47,11,65,16,21,64, 7,
38,55, 5,28,38,20,24,27,31, 9, 9,11,56,36,56,15,51,33,70,32,
5,23,63,30,53,12,58,54,36,20,74,34,70,25,65, 4,10,58,37,56,
6, 0,70,70,28,40,67,36,23,23,62,62,62, 2,34, 4,12,56, 1, 7,
4,70,65, 7,30,40,13,22, 0,18,64,13,26, 1,16,33,22,30,53,53,
7,61,40, 9,59, 7,12,46,50, 0,52,19,52,51,51,14,27,51, 5, 0,
41,53,19)
event1 = c(0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,
1,0,0,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0,1,1,
1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0,
0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,
0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,0,0,0,0,0,
1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,0,1,1,0,0,
1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,1,0,1,0,0,0,0,1,1,1,1,0,0,0,1,1,0,0,
1,1,1,1,0,0,1,0,1,1,1,1,1,1,1,0,1,1,0,1,
0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,
0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,0,0,1,
1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,1,0,0,1,0,1,0,1,1,0,1,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,
1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,1,
1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,
0,0,1)
event2 = c(0,1,1,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,1,
0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,1,1,0,0,0,
0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,1,0,1,0,0,
0,0,1,0,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,
1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,
0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,1,
0,1,0,0,1,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,
1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,
0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,1,
0,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0,
1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,
0,0,0,0,1,0,1,0,1,1,1,1,0,1,1,1,0,1,1,1,
1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,1,
0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,
1,1,0,0,1,0,0,0,0,1,1,1,1,0,1,1,1,0,1,0,
1,1,1,1,1,1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,
1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,
0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,
0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,
1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,
0,0,0,0,1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,
0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,1,
1,0,0)
library(Bivariate.Pareto)
set.seed(10)
MLE.Frank.Pareto(t.event,event1,event2,Theta = -5)