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

Description Usage Arguments Value Author(s) References Examples

View source: R/Clayton.Markov.MLE.R

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

1
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

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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.