surveillance: arlCusum – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

arlCusum

Calculation of Average Run Length for discrete CUSUM schemes

Description

Calculates the average run length (ARL) for an upward CUSUM scheme for discrete distributions (i.e. Poisson and binomial) using the Markov chain approach.

Usage

arlCusum(h=10, k=3, theta=2.4, distr=c("poisson","binomial"),
         W=NULL, digits=1, ...)

Arguments

`h`	decision interval
`k`	reference value
`theta`	distribution parameter for the cumulative distribution function (cdf) F, i.e. rate λ for Poisson variates or probability p for binomial variates
`distr`	`"poisson"` or `"binomial"`

`W`	Winsorizing value `W` for a robust CUSUM, to get a nonrobust CUSUM set `W` > `k`+`h`. If `NULL`, a nonrobust CUSUM is used.
`digits`	`k` and `h` are rounded to `digits` decimal places
`...`	further arguments for the distribution function, i.e. number of trials `n` for binomial cdf

Value

Returns a list with the ARL of the regular (zero-start) and the fast initial response (FIR) CUSUM scheme with reference value k, decision interval h for X \sim F(θ), where F is the Poisson or binomial CDF.

`ARL`	one-sided ARL of the regular (zero-start) CUSUM scheme
`FIR.ARL`	one-sided ARL of the FIR CUSUM scheme with head start \frac{\code{h}}{2}

Source

Based on the FORTRAN code of

Hawkins, D. M. (1992). Evaluation of Average Run Lengths of Cumulative Sum Charts for an Arbitrary Data Distribution. Communications in Statistics - Simulation and Computation, 21(4), p. 1001-1020.

surveillance

Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

v1.19.1

GPL-2

Authors

Michael H<f6>hle [aut, ths] (<https://orcid.org/0000-0002-0423-6702>), Sebastian Meyer [aut, cre] (<https://orcid.org/0000-0002-1791-9449>), Michaela Paul [aut], Leonhard Held [ctb, ths], Howard Burkom [ctb], Thais Correa [ctb], Mathias Hofmann [ctb], Christian Lang [ctb], Juliane Manitz [ctb], Andrea Riebler [ctb], Daniel Saban<e9>s Bov<e9> [ctb], Ma<eb>lle Salmon [ctb], Dirk Schumacher [ctb], Stefan Steiner [ctb], Mikko Virtanen [ctb], Wei Wei [ctb], Valentin Wimmer [ctb], R Core Team [ctb] (A few code segments are modified versions of code from base R)

Initial release

2021-03-30