Interquartile Range (robust spread)

Computes the interquartile range (IQR) of a one-dimensional signal – the spread of the middle 50%, \(Q_3 - Q_1\) – a robust, quantile-based measure of dispersion that ignores the tails entirely. The quartiles use R's default type-7 quantile (the same linear interpolation as scipy.stats.iqr and numpy.percentile), so the result matches both bit-for-bit.

Usage

interquartileRange(x, type = 7L)

Arguments

x

A numeric vector (the time series).

type

Quantile algorithm passed to quantile (default 7, matching base R, scipy and numpy).

Value

A single numeric value, the interquartile range.

Details

A quantile-based robust spread that complements medianAbsDev (a deviation-based robust scale) and signalMoments (the classical SD). For approximately Gaussian data, \(\mathrm{IQR} / (2\,\Phi^{-1}(0.75))\) (\(\approx \mathrm{IQR}/1.349\)) is a robust estimate of the SD; a value well below the SD flags a skewed or heavy-tailed distribution.

See also

medianAbsDev for the deviation-based robust scale, signalMoments for the classical moments.

Examples

interquartileRange(c(1, 2, 3, 4, 100))   # robust to the outlier
#> [1] 2
interquartileRange(rnorm(1000)) / 1.349  # ~1 (robust SD estimate)
#> [1] 1.006017