Hosking and Wallis Data Set, Table 3.3

Description

The data on annual maximum streamflow at 17 sites with largest drainage area basins in southeastern USA contains the sample L-moments ratios (L-CV, L-skewness and L-kurtosis) as used by Hosking and Wallis (1997) to illustrate the discordancy measure in regional freqency analysis (RFA).

Usage

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Format

A data frame with 17 observations on the following 3 variables.

L-CV

L-coefficient of variation

L-skewness

L-coefficient of skewness

L-kurtosis

L-coefficient of kurtosis

Details

The sample L-moment ratios (L-CV, L-skewness and L-kurtosis) of a site are regarded as a point in three dimensional space.

Source

Hosking, J. R. M. and J. R. Wallis (1997), Regional Frequency Analysis: An Approach Based on L-moments. Cambridge University Press, p.51, Table 3.3

References

Neykov, N.M., Neytchev, P.N., Van Gelder, P.H.A.J.M. and Todorov V. (2007), Robust detection of discordant sites in regional frequency analysis, Water Resources Research, 43, W06417, doi:10.1029/2006WR005322, http://www.agu.org/pubs/crossref/2007/2006WR005322.shtml

Examples

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    data(lmom33)

    # plot a matrix of scatterplots
    pairs(lmom33,
          main="Hosking and Wallis Data Set, Table 3.3",
          pch=21,
          bg=c("red", "green3", "blue"))

    mcd<-CovMcd(lmom33)
    mcd
    plot(mcd, which="dist", class=TRUE)
    plot(mcd, which="dd", class=TRUE)

    ##  identify the discordant sites using robust distances and compare 
    ##  to the classical ones
    mcd <- CovMcd(lmom33)
    rd <- sqrt(getDistance(mcd))
    ccov <- CovClassic(lmom33)
    cd <- sqrt(getDistance(ccov))
    r.out <- which(rd > sqrt(qchisq(0.975,3)))
    c.out <- which(cd > sqrt(qchisq(0.975,3)))
    cat("Robust: ", length(r.out), " outliers: ", r.out,"\n")
    cat("Classical: ", length(c.out), " outliers: ", c.out,"\n")

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