Statistics for Skewness-adjusted Boxplots

Computes the “statistics” for producing boxplots adjusted for skewed distributions as proposed in Hubert and Vandervieren (2008), see adjbox.

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

Arguments

x: 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.

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.

Value

A list with the components

stats: a 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.
n: the number of observations
conf: the lower and upper extremes of the ‘notch’ (if(do.conf)). See boxplot.stats.
fence: length 2 vector of interval boundaries which define the non-outliers, and hence the whiskers of the plot.
out: the values of any data points which lie beyond the fence, and hence beyond the extremes of the whiskers.

Author

R Core Development Team (boxplot.stats); adapted by Tobias Verbeke and Martin Maechler.

Note

The code only slightly modifies the code of R's boxplot.stats.

Examples