fournum {sn}

Four-number summary of a numeric vector

Description

Returns a quantile-based four-number summary of the input data

Usage

fournum(x, na.rm = TRUE, ...)

Arguments

x

a numeric vector, maybe including NAs and +/-Inf's. At least 8 not-NA values are required. It works with objects which can be coerced to vector.

na.rm

logical; if TRUE, all NA and NaNs are dropped, before the statistics are computed.

...

optional arguments passed to quantile

Details

Function quantile is used to compute 7 octiles of x, that is, quantiles of level (1:7)/8, denoted oct[1:7], and derive four summary quantities:

1. the median, which corresponds to oct[4],

2. the ‘(coefficient of) quartile deviation’ or semi-interquantile range: (oct[6] - oct[2])/2;

3. the Galton-Bowley measure of asymmetry, that is, skewness: (oct[6] - 2 * oct[4] + oct[2])/(oct[6] - oct[2]);

4. the Moors measure of kurtosis: (oct[7] - oct[5] + oct[3] - oct[1])/(oct[6] - oct[2])

The term ‘coefficient of quartile deviation’ is adopted from the Encyclopedia of Statistical Sciences; see the references below. What is called Galton-Bowley measure here is often named ‘Bowley's measure’, but some sources attribute it to Francis Galton. For the Moors measure, see Moors (1988).

Value

a vector of length four containing the median, the quartile deviation, the Galton-Bowley measure and the Moors measure. However, if x does not contain at least 8 values (after removing NAs), rep(NA,4) is returned.

Note

Computation of octiles makes real sense only if length(x) is substantially larger than 8.

Author(s)

Adelchi Azzalini

References

‘Quartile deviation, coefficient of’, in: Encyclopedia of Statistical Sciences, 2nd edition (2006). Editors: Samuel Kotz (Editor-in-Chief), Campbell B. Read, N. Balakrishnan, Brani Vidakovic. Volume 10, p.6743.

‘Skewness, Bowleys's measures of’, in: Encyclopedia of Statistical Sciences, 2nd edition (2006). Editors: Samuel Kotz (Editor-in-Chief), Campbell B. Read, N. Balakrishnan, Brani Vidakovic. Volume 12, p.7771-7773.

Moors, J.J.A. (1988). A quantile alternative for kurtosis. Source: Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 37, pp. 25-32

See Also

quantile, fivenum, IQR

Examples

fournum(datasets::rivers)