sen.mean {lmomco}R Documentation

Sen's Weighted Mean Statistic

Description

The Sen weighted mean statistic mathcal{S}_{n,k} is a robust estimator of the mean of a distribution.

mathcal{S}_{n,k} = {n choose 2k+1}^{-1} sum_{i=1}^n {i - 1 choose k} {n - i choose k } X_{i:n}

where X_{i:n} are the order statistics and k is a weighting or trimming parameter.

Note that mathcal{S}_{n,0} = μ = overline{X}_n or the arithmetic mean and mathcal{S}_{n,k} is the sample median if either n is even and k = (n/2) - 1 or n is odd and k = (n-1)/2.

Usage

sen.mean(x,k=0)

Arguments

x A vector of data values that will be reduced to non-missing values.
k A weighting or trimming parameter 0 < k < (n-1)/2.

Value

An R list is returned.

sen The sen mean mathcal{S}_{n,k}
source An attribute identifying the computational source of Sen's Weighted Mean: “sen.mean”.

Author(s)

W.H. Asquith

References

Jurečková, J., and Picek, J., 2006, Robust statistical methods with R: Boca Raton, Fla., Chapman and Hall/CRC, ISBN 1–58488–454–1, 197~p.

Sen, P.K., 1964, On some properties of the rank-weighted means: Journal Indian Society of Agricultural Statistics: vol.~16, pp.~51–61.

See Also

TLmoms, gini.mean.diff

Examples

fake.dat <- c(123,34,4,654,37,78)
sen.mean(fake.dat); mean(fake.dat) # These should be the same values

sen.mean(fake.dat, k=(length(fake.dat)/2) - 1); median(fake.dat) # Again, same values

# Finally, the sen.mean() is like a symmetrically trimmed TL-moment
# Let us demonstrate by computed a two sample trimming for each side
# for a Normal distribution having a mean of 100.
fake.dat <- rnorm(20, mean=100)
lmr <- TLmoms(fake.dat, trim=2)
sen <- sen.mean(fake.dat, k=2)

print(abs(lmr$lambdas[1] - sen$sen)) # zero is returned

[Package lmomco version 0.96.3 Index]