# MLE.Frank.Pareto.com: Maximum likelihood estimation for bivariate dependent... In Bivariate.Pareto: Bivariate Pareto Models

## 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.