Description Usage Arguments Value Author(s) References Examples
View source: R/Joe.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 Joe copula and the marginal (stationary) distribution follows the normal distribution.
1 | Joe.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 Takeshi Emura
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 4 5 6 7 8 9 10 | n=1000
alpha=2.856 ### Kendall's tau =0.5 ###
mu=2
sigma=1
Y=Joe.Markov.DATA(n,mu,sigma,alpha)
mean(Y)
sd(Y)
cor(Y[-1],Y[-n],method="kendall")
Joe.Markov.MLE(Y,k=2)
|
[1] 1.869801
[1] 0.9572086
[1] 0.4607553
$estimates
mu sigma alpha UCL LCL
1.8958440 0.9983598 2.6785176 3.8925637 -0.1008757
$out_of_control
[1] 4 43 71 96 115 116 122 123 124 211 248 264 297 298 300 311 376 430 434
[20] 442 487 553 562 594 603 621 672 701 793 822 839 901 946 947 948 949 950 968
[39] 969 976
$Gradient
[1] -6.821210e-15 -5.306866e-14 6.593837e-15
$Hessian
[,1] [,2] [,3]
[1,] -0.5411087 -0.2183230 0.1971793
[2,] -0.2183230 -2.1813517 0.3915524
[3,] 0.1971793 0.3915524 -0.1371003
$Mineigenvalue_Hessian
[1] -2.289899
$CM.test
[1] 0.1091633
$KS.test
[1] 0.02844239
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