Description Usage Arguments Details Value References Examples
View source: R/MLE.SN.Pareto.R
Maximum likelihood estimation for bivariate dependent competing risks data under the SNBP distribution (Sankaran and Nair, 1993).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | MLE.SN.Pareto(
t.event,
event1,
event2,
Alpha0,
Alpha1.0 = 1,
Alpha2.0 = 1,
Gamma.0 = 1,
epsilon = 1e-05,
d = exp(10),
r.1 = 6,
r.2 = 6,
r.3 = 6
)
|
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. |
Alpha0 |
Copula parameter α_{0} with restricted range. |
Alpha1.0 |
Initial guess for the scale parameter α_{1} with default value 1. |
Alpha2.0 |
Initial guess for the scale parameter α_{2} 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}. |
d |
Positive tunning parameter in the NR algorithm with default value e^{10}. |
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. |
The admissible range of Alpha0
(α_{0}) is 0 ≤q α_{0} ≤q (γ+1) α_{1} α_{2}.
To adapt our functions to dependent censoring models in Emura and Chen (2018), one can simply set event2
= 1-event1
.
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). |
Gamma |
Common positive shape parameter for the Pareto margins. |
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. |
Sankaran PG, Nair NU (1993), A bivariate Pareto model and its applications to reliability, Naval Research Logistics, 40(7): 1013-1020.
Emura T, Chen Y-H (2018) Analysis of Survival Data with Dependent Censoring, Copula-Based Approaches, JSS Research Series in Statistics, Springer, Singapore.
Shih J-H, Lee W, Sun L-H, Emura T (2019), Fitting competing risks data to bivariate Pareto models, Communications in Statistics - Theory and Methods, 48:1193-1220.
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.SN.Pareto(t.event,event1,event2,Alpha0 = 7e-5)
|
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