detectChangePointBatch: Detect a Single Change Point in a Sequence

Description

This function is used to detect a single change point in a sequence of observations using the Change Point Model (CPM) framework for batch (Phase I) change detection. The observations are processed in one batch and information is returned regarding whether the sequence contains a change point. A full description of the CPM framework can be found in the papers cited in the reference section. For a fuller overview of this function including a description of the CPM framework and examples of how to use the various functions, please consult the package manual "Parametric and Nonparametric Sequential Change Detection in R: The cpm Package" available from www.gordonjross.co.uk

Usage

detectChangePointBatch(x, cpmType, alpha=0.05, lambda=NA)

Arguments

Value

xThe sequence of observations which was processed.changeDetectedTRUE if $D_n$ exceeds the value of $h_n$ associated with alpha, otherwise FALSE.changePointassuming a change was detected, this stores the most likely location of the change point, defined as the value of k which maximized $D_kt$. If no change is detected, this will be equal to 0.thresholdThe value of $h_n$ which corresponds to the specified alpha.DsThe sequence of $D_kt$ test statistics.

References

Hawkins, D. , Zamba, K. (2005) -- A Change-Point Model for a Shift in Variance, Journal of Quality Technology, 37, 21-31

Hawkins, D. , Zamba, K. (2005b) -- Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation, Technometrics, 47(2), 164-173 Hawkins, D., Qiu, P., Kang, C. (2003) -- The Changepoint Model for Statistical Process Control, Journal of Quality Technology, 35, 355-366. Ross, G. J., Tasoulis, D. K., Adams, N. M. (2011) -- A Nonparametric Change-Point Model for Streaming Data, Technometrics, 53(4) Ross, G. J., Adams, N. M. (2012) -- Two Nonparametric Control Charts for Detecting Arbitary Distribution Changes, Journal of Quality Technology, 44:102-116 Ross, G. J., Adams, N. M. (2013) -- Sequential Monitoring of a Proportion, Computational Statistics, 28(2)

Ross, G. J., (2014) -- Sequential Change Detection in the Presence of Unknown Parameters, Statistics and Computing 24:1017-1030 Ross, G. J., (2015) -- Parametric and Nonparametric Sequential Change Detection in R: The cpm Package, Journal of Statistical Software, forthcoming

Examples

Run this code

## Use a Student-t CPM to detect a mean shift in a stream of Gaussian 
     ## random variables which occurs after the 100th observation
     x <- c(rnorm(100,0,1),rnorm(1000,1,1))
     detectChangePointBatch(x,"Student",alpha=0.05)


     ## Use a Mood CPM to detect a scale shift in a stream of Student-t 
     ## random variables which occurs after the 100th observation
     x <- c(rt(100,5),rt(1000,5*2))
     detectChangePointBatch(x,"Mood",alpha=0.05)

     ## Use a FET CPM to detect a parameter shift in a stream of Bernoulli 
     ##observations. In this case, the lambda parameter acts to reduce the 
     ##discreteness of the test statistic.
     x <- c(rbinom(100,1,0.2), rbinom(1000,1,0.5))
     detectChangePointBatch(x,"FET",alpha=0.05,lambda=0.3)