Clayton.Markov.MLE: Maximum Likelihood Estimation and Statistical Process Control...

In Copula.Markov: Copula-Based Estimation and Statistical Process Control for Serially Correlated Time Series

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(Y, k = 3, D = 1, plot = TRUE,GOF=FALSE,method = "nlm")

Arguments

Y	vector of datasets
k	constant determining the length between LCL and UCL (k=3 corresponds to 3-sigma limit)
D	diameter for U(-D, D) used in randomized Newton-Raphson
plot	show the control chart if TRUE
GOF	show the model diagnostic plot if TRUE
method	apply "nlm" or "Newton" method

Value

mu	estimate, SE, and 95 percent CI
sigma	estimate, SE, and 95 percent CI
alpha	estimate, SE, and 95 percent CI
Control_Limit	Center = mu, 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)

Long TH, Huang XW and Emura T

References

Emura T, Long TH, Sun LH (2017), R routines for performing estimation and statistical process control under copula-based time series models, Communications in Statistics - Simulation and Computation, 46 (4): 3067-87

Long TH and Emura T (2014), A control chart using copula-based Markov chain models, Journal of the Chinese Statistical Association 52 (No.4): 466-96

Examples

set.seed(1)
Y=Clayton.Markov.DATA(n=1000,mu=0,sigma=1,alpha=2)
Clayton.Markov.MLE(Y,plot=TRUE)

Example output

$estimates
         mu       sigma       alpha         UCL         LCL 
 0.04163666  0.99659124  1.94226139  3.03141039 -2.94813707 

$out_of_control
 [1] 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
[20] 916 917 918 919 920 921 923 988

$Gradient
[1] 1.136016e-12 8.362235e-13 1.030200e-12

$Hessian
           [,1]       [,2]       [,3]
[1,] -0.5079525  0.2523475 -0.1862500
[2,]  0.2523475 -2.3704581  0.4308937
[3,] -0.1862500  0.4308937 -0.1369371

$Mineigenvalue_Hessian
[1] -2.491013

$CM.test
[1] 0.1322401

$KS.test
[1] 0.04030006

Copula.Markov documentation built on Nov. 29, 2021, 9:07 a.m.