skippedMean {MKdescr}

Hyber-type Skipped Mean and SD

Description

Computes Huper-type Skipped Mean and SD.

Usage

skippedMean(x, na.rm = FALSE, constant = 3.0)
skippedSD(x, na.rm = FALSE, constant = 3.0)

Arguments

x

a numeric vector.

na.rm

logical. Should missing values be removed?

constant

multiplier for outlier identification; see details below.

Details

The Huber-type skipped mean and is very close to estimator X42 of Hampel (1985), which uses 3.03 x MAD. Quoting Hampel et al. (1986), p. 69, the X42 estimator is "frequently quite reasonable, according to present preliminary knowledge".

For computing the Huber-type skipped mean, one first computes median and MAD. In the next step, all observations outside the interval [median - constant x MAD, median + constant x MAD] are removed and arithmetic mean and sample standard deviation are computed on the remaining data.

Author(s)

Matthias Kohl [e-mail]

References

Hampel, F.R. (1985). The breakdown points of the mean combined with some rejection rules. Technometrics, 27: 95-107.

Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A (1986). Robust statistics. The approach based on influence functions. New York: Wiley.

See Also

mean, sd, median, mad.

Examples

## normal data
x <- rnorm(100)
mean(x)
median(x)
skippedMean(x)

sd(x)
mad(x)
skippedSD(x)

## Tukey's gross error model
## (1-eps)*Norm(mean, sd = sigma) + eps*Norm(mean, sd = 3*sigma)
ind <- rbinom(100, size = 1, prob = 0.1)
x.err <- (1-ind)*x + ind*rnorm(100, sd = 3)
mean(x.err)
median(x.err)
skippedMean(x.err)

sd(x.err)
mad(x.err)
skippedSD(x.err)