cpm (version 2.0)

getBatchThreshold: Returns the Threshold Associated with a Type I Error Probability .

Description

When performing Phase I analysis within the CPM framework for a sequence of length n, the null hypothesis of no change is rejected if $D_n > h_n$ for some threshold $h_n$. Typically this threshold is chosen to be the upper alpha quantile of the distribution of $D_n$ under the null hypothesis of no change. Given a particular choice of alpha and n, this function returns the associated $h_n$ threshold. Because these thresholds are laborious to compute, the package contains pre-computed values of $h_n$ for alpha = 0.05, 0.01, 0.005 and 0.001, and for $n < 10000$.

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

getBatchThreshold(cpmType, alpha, n, lambda=0.3)

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, In Press Ross, G. J., Adams, N. M. (2013) -- Sequential Monitoring of a Proportion, Computational Statistics, 28(2)

Ross, G. J., (2013) -- Sequential Change Detection in the Presence of Unknown Parameters (to appear)

See Also

detectChangePointBatch.

Examples

## Returns the threshold for n=1000, alpha=0.05 and the Mann-Whitney CPM
     h <- getBatchThreshold("Mann-Whitney", 0.05, 1000)