mad {complexlm}

Median Absolute Deviation, compatible with complex variables

Description

Median absolute deviation, adapted to operate on complex data as well as numeric. In the later case it simply calls stats::mad(). For complex x it uses the geometric median, pracma::geo_median(), as the center, then returns the median absolute difference between center and each element of x, multiplied by constant.

Usage

mad(
  x,
  center = median(x),
  constant = 1.4826,
  na.rm = FALSE,
  low = FALSE,
  high = FALSE
)

Arguments

x

a numeric or complex vector.

center

optional, numeric or complex. The center about which to calculate MAD. Defaults to median for numeric, and geo_median for complex.

constant

a constant by which to multiply the median absolute deviation from center. Default is 1.4826, which is the inverse of the 3/4 quantile for the normal distribution.

na.rm

logical. Should NAs be removed from x before calculating.

low

logical. If TRUE, compute the "lo-median", i.e., for even sample size, do not average the two middle values, but take the smaller one. Not used if x is complex.

high

logical. If TRUE, compute the "hi-median", i.e., take the larger of the two middle values for even sample size. Not used if x is complex.

Value

numeric. The median absolute deviation (MAD) from center.

Note

The concept of quantile requires ordering to be defined, which the complex numbers lack. The usefulness of multiplying by constant is thus called into question. However, for no more rigorous reason than consistency, the default behavior of this function is to do so.

See Also

median.complex, stats::mad

Examples

set.seed(4242)
n <- 8
foo <- complex(real = rnorm(n), imaginary = rnorm(n))
mad(foo)