MLE.Frank.Pareto.com: Maximum likelihood estimation for bivariate dependent...

Description Usage Arguments Details Value References Examples

View source: R/MLE.Frank.Pareto.com.R

Description

Maximum likelihood estimation for bivariate dependent competing risks data under the Frank copula with the common Pareto margins.

Usage

1
2
3
MLE.Frank.Pareto.com(t.event, event1, event2, Theta.0 = 1, Alpha.0 = 1,
  Gamma.0 = 1, epsilon = 1e-05, r.1 = 13, r.2 = 3, r.3 = 3,
  bootstrap = FALSE, B = 200)

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.0

Initial guess for the copula parameter θ.

Alpha.0

Initial guess for the common scale parameter α with default value 1.

Gamma.0

Initial guess for the common shape parameter γ with default value 1.

epsilon

Positive tunning parameter in the NR algorithm with default value 10^{-5}.

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.

bootstrap

Perform parametric bootstrap if TRUE.

B

Number of bootstrap replications.

Details

The parametric bootstrap method requires the assumption of the uniform censoring distribution. One must notice that such assumption is not always true in real data analysis.

Value

n

Sample size.

count

Iteration number.

random

Randomization number.

Theta

Copula parameter.

Theta.B

Copula parameter (SE and CI are calculated by parametric bootstrap method).

Alpha

Common positive scale parameter for the Pareto margin.

Alpha.B

Common positive scale parameter for the Pareto margin (SE and CI are calculated by parametric bootstrap method).

Gamma

Common positive shape parameter for the Pareto margin.

Gamma.B

Common positive shape parameter for the Pareto margin (SE and CI are calculated by parametric bootstrap method).

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
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.com(t.event,event1,event2,bootstrap = FALSE)

Bivariate.Pareto documentation built on April 2, 2018, 5:03 p.m.