Description Usage Arguments Value Author(s) References Examples
View source: R/Clayton.Markov.MLE.R
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.
1 | Clayton.Markov.MLE(Y, k = 3, D = 1, plot = TRUE,GOF=FALSE,method = "nlm")
|
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 |
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 |
Long TH, Huang XW and Emura T
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
1 2 3 | set.seed(1)
Y=Clayton.Markov.DATA(n=1000,mu=0,sigma=1,alpha=2)
Clayton.Markov.MLE(Y,plot=TRUE)
|
$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
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