MKdescr (version 0.4)

skippedMean: 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.

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

# NOT RUN {
## 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)
# }