FrankFrank.Weibull.MLE {Copula.Markov.survival} R Documentation

## Parameter estimation based on the Frank copula for serial dependence and the Frank copula for dependent censoring with the Weibull distributions

### Description

Perform two-stage estimation based on the Frank copula C_theta for serial dependence and the Frank copula tilde(C)_alpha for dependent censoring with the marginal distributions Weib(scale1, shape1) and Weib(scale2, shape2). The jackknife method estimates the asymptotic covariance matrix. Parametric bootstrap is applied while doing Kolmogorov-Smirnov tests and Cramer-von Mises test. The guide for using this function shall be explained by Huang (2019), and Huang, Wang and Emura (2020).

### Usage

```FrankFrank.Weibull.MLE(subject, t.event, event, t.death, death, stageI, Weibull.plot,
jackknife, plot, GOF, GOF.plot, rep.GOF, digit)
```

### Arguments

 `subject` a vector for numbers of subject `t.event` a vector for event times `event` a vector for event indicator (=1 if recurrent; =0 if censoring) `t.death` a vector for death times `death` a vector for death vindicator (=1 if death; =0 if censoring) `stageI` an option to select MLE or LSE method for the 1st-stage optimization `Weibull.plot` if TRUE, show the Weibull probability plot `jackknife` if TRUE, the jackknife method is used for estimate covariance matrix (default = TRUE) `plot` if TRUE, the plots for marginal distributions are shown (default = FALSE) `GOF` if TRUE, show the p-values for KS-test and CvM-test `GOF.plot` if TRUE, show the model diagnostic plot `rep.GOF` repetition number of parametric bootstrap `digit` accurate to some decimal places

### Details

When jackknife=FALSE, the corresponding standard error and confidence interval values are shown as NA.

### Value

A list with the following elements:

 `Sample_size` Sample size N `Case` Count for event occurences `scale1` Scale parameter for Weib(scale1, shape1) `shape1` Shape parameter for Weib(scale1, shape1) `scale2` Scale parameter for Weib(scale2, shape2) `shape2` Shape parameter for Weib(scale2, shape2) `theta` Copula parameter for the Frank copula C_theta `alpha` Copula parameter for the Frank copula tilde(C)_alpha `COV` Asymptotic covariance estimated by the jackknife method `KS` Kolmogorov-Smirnov test statistics `p.KS` P-values for Kolmogorov-Smirnov tests `CM` Cramer-von Mises test statistics `p.CM` P-values for Cramer-von Mises tests `Convergence` Convergence results for each stage `Jackknife_error` Count for error in jackknife repititions `Log_likelihood` Log-likelihood values

Xinwei Huang

### Examples

```data = FrankFrank.Weibull.data(N = 300, scale1 = 1, shape1 =0.5, theta = 2,
scale2 = 0.45, shape2 = 0.5, alpha = 2, b = 10, l = 300)

FrankFrank.Weibull.MLE(subject = data\$Subject,
t.event = data\$T_ij, event = data\$delta_ij,
t.death = data\$T_i_star, death = data\$delta_i_star,
jackknife= TRUE, plot = TRUE)

```

[Package Copula.Markov.survival version 1.0.0 Index]