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

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, Emura T (2021-), Computational methods for a copula-based Markov chain model with a 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)