adjboxStats: Statistics for Skewness-adjusted Boxplots

Description

Computes the statistics for producing boxplots adjusted for skewed distributions as proposed in Hubert and Vandervieren (2004), see adjbox.

Usage

adjboxStats(x, coef = 1.5, a = -4, b = 3, do.conf = TRUE, do.out = TRUE,
            ...)

Arguments

a numeric vector for which adjusted boxplot statistics are computed.

coef

number determining how far whiskers extend out from the box, see boxplot.stats.

a, b

scaling factors multiplied by the medcouple mc() to determine outlyer boundaries; see the references.

do.conf,do.out

logicals; if FALSE, the conf or out component respectively will be empty in the result.

...

further optional arguments to be passed to mc(), such as doReflect.

Value

A list with the components
statsa vector of length 5, containing the extreme of the lower whisker, the lower hinge, the median, the upper hinge and the extreme of the upper whisker.
nthe number of observations
confthe lower and upper extremes of the notch (if(do.conf)). See boxplot.stats.
fencelength 2 vector of interval boundaries which define the non-outliers, and hence the whiskers of the plot.
outthe values of any data points which lie beyond the fence, and hence beyond the extremes of the whiskers.

Details

Given the quartiles $Q_1$, $Q_3$, the interquartile range $\Delta Q := Q_3 - Q_1$, and the medcouple $M :=$mc(x), $c =$coef, the fence is defined, for $M \ge 0$ as $$[Q_1 - c e^{a \cdot M}\Delta Q, Q_3 + c e^{b \cdot M}\Delta Q],$$ and for $M < 0$ as $$[Q_1 - c e^{-b \cdot M}\Delta Q, Q_3 + c e^{-a \cdot M}\Delta Q],$$ and all observations x outside the fence, the potential outliers, are returned in out.

Note that a typo in robustbase version up to 0.7-8, for the (rare left-skewed) case where mc(x) < 0, lead to a fence not wide enough in the upper part, and hence less outliers there.

Examples

Run this code

data(condroz)
adjboxStats(ccA <- condroz[,"Ca"])
adjboxStats(ccA, doReflect = TRUE)# small difference in fence

## Test reflection invariance [was not ok, up to and including robustbase_0.7-8]
a1 <- adjboxStats( ccA, doReflect = TRUE)
a2 <- adjboxStats(-ccA, doReflect = TRUE)

nm1 <- c("stats", "conf", "fence")
stopifnot(all.equal(       a1[nm1],
                    lapply(a2[nm1], function(u) rev(-u))),
          all.equal(a1[["out"]], -a2[["out"]]))