Clayton.Markov.GOF {Copula.Markov}

A goodness-of-fit test for the marginal normal distribution.

Description

Perform a parametric bootstrap test based on the Cramer-von Mises and Kolmogorov-Smirnov statistics as proposed by Huang and Emura (2019).

Usage

Clayton.Markov.GOF(Y, k = 3, D = 1, B = 200,GOF.plot=FALSE, method = "Newton")

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

B

the number of Bootstrap replications

GOF.plot

if TRUE, show the model diagnostic plots for B bootstrap replications

method

Newton-Raphson method or nlm can be chosen

Value

CM

The Cramer-von Mises statistic and its P-value

KS

The Kolmogorov-Smirnov statistic and its P-value

CM.boot

Bootstrap values of the Cramer-von Mises statistics

KS.boot

Bootstrap values of the Kolmogorov-Smirnov statistics

Author(s)

Takeshi Emura

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

Huang XW, Emura T (2021), Model diagnostic procedures for copula-based Markov chain models for statistical process control, Communications in Statistics - Simulation and Computation, doi: 50(8):2345-67

Examples

set.seed(1)
Y=Clayton.Markov.DATA(n=1000,mu=0,sigma=1,alpha=2)
Clayton.Markov.GOF(Y,B=5,GOF.plot=TRUE)