Clayton.Markov.MLE.binom {Copula.Markov} R Documentation

## Maximum Likelihood Estimation and Statistical Process Control Under the Clayton Copula

### Description

The maximum likelihood estimates are produced and the Shewhart control chart is drawn with k-sigma control limits (e.g., 3-sigma). The dependence model follows the Clayton copula and the marginal (stationary) distribution follows the normal distribution.

### Usage

```Clayton.Markov.MLE.binom(Y, size, k = 3, method="nlm", plot = TRUE, GOF=FALSE)
```

### Arguments

 `Y` vector of observations `size` numbe of binomial trials `method` nlm or Newton `k` constant determining the length between LCL and UCL (k=3 corresponds to 3-sigma limit) `plot` show the control chart if TRUE `GOF` show the model diagnostic plot if TRUE

### Value

 `p ` estimate, SE, and 95 percent CI `alpha ` estimate, SE, and 95 percent CI `Control_Limit ` Center = n*p, LCL = mu - k*sigma, UCL = mu + k*sigma `out_of_control ` IDs for out-of-control points `Gradient ` gradients (must be zero) `Hessian ` Hessian matrix `Eigenvalue_Hessian ` Eigenvalues for the Hessian matrix `KS.test ` KS statistics `CM.test ` CM statistics `log_likelihood ` Log-likelihood value for the estimation

### Author(s)

Huang XW, Emura T

### References

Chen W (2018) Copula-based Markov chain model with binomial data, NCU Library

Huang XW, Chen W, Emura T (2019-), Likelihood-based inference for a copula-based Markov chain model with binomial time series, in review

### Examples

```size=50
prob=0.5
alpha=2
set.seed(1)
Y=Clayton.Markov.DATA.binom(n=500,size,prob,alpha)
Clayton.Markov.MLE.binom(Y,size=size,k=3,plot=TRUE)
```

[Package Copula.Markov version 2.8 Index]