RSlo: Rosner RST Test Adjusted for Low Outliers
In wasquith-usgs/MGBT: Multiple Grubbs-Beck Low-Outlier Test

Description Usage Arguments Value Note Author(s) Source References See Also Examples

The Rosner (1975) method or the essence of the method, given the order statistics x_{[1:n]} ≤ x_{[2:n]} ≤ \cdots ≤ x_{[(n-1):n]} ≤ x_{[n:n]}, is the statistic:

RS_r = \frac{ x_{[r:n]} - \mathrm{mean}\{x_{[(r+1)\rightarrow(n-r):n]}\} } {√{\mathrm{var}\{x_{[(r+1)\rightarrow(n-r):n]}\}}}\mbox{,}

1	RSlo(x, r, n=length(x))

`x`	The data values and note that base-10 logarithms of these are not computed internally;
`r`	The number of truncated observations; and
`n`	The number of observations.

The value for RS_r.

Regarding n=length(x), it is not clear that TAC intended n to be not equal to the sample size. TAC chose to not determine the length of x internally to the function but to have it available as an argument. Also MGBTcohn2011 and BLlo were similarly designed.

W.H. Asquith consulting T.A. Cohn sources

LowOutliers_jfe(R).txt and LowOutliers_wha(R).txt—Named RST

Cohn, T.A., 2013–2016, Personal communication of original R source code: U.S. Geological Survey, Reston, Va.

Rosner, Bernard, 1975, On the detection of many outliers: Technometrics, v. 17, no. 2, pp. 221–227.

MGBTcohn2011, BLlo

## Not run: 
testMGBvsN3 <- function(n=100, maxr=n/2, nrep=10000) { # TAC named function
   for(r in 1:maxr) {
      set.seed(123457)
      res1 <- replicate(nrep, { x <- sort(rnorm(n))
                 c(MGBTcohn2011(x,r),BLlo(x,r),RSlo(x,r)) })
      r1 <- rank(res1[1,]); r2 <- rank(res1[2,]); r3 <- rank(res1[3,])
      v <- quantile(r1,.1); h <- quantile(r2,.1)
      plot(r1,r2)
      abline(v=v, col=2); abline(h=h, col=2)
      message(' BLlo ',r, " ", cor(r1,r2), " ", mean((r1 <= v) & (r2 <= h)))
      v <- quantile(r1,.1); h <- quantile(r2,.1)
      plot(r1,r3)
      abline(v=v, col=2); abline(h=h, col=2)
      message('RSTlo ',r, " ", cor(r1,r3), " ", mean((r1 <= v) & (r3 <= h)))
   }
}
testMGBvsN3() #
## End(Not run)