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MEDABSDEV

MEDABSDEV

Name


  medabsdev

Purpose


  This function returns a data set's median absolute deviation
  from the median. That is, it returns
    median( |data - median(data) | )
  It is a proxy for the standard deviation, but is more resistent
  against outliers.

Category


  Statistics

Calling Sequence


  result = medabssdev(data, [/sigma], [/even])

Inputs


  data: An array of data

Keyword Parameters


  sigma: If set, divide the median absolute deviation by
  inverseErf(0.5) * sqrt(2). This scales the MAD to an approximation
  for sigma (assuming a Gaussian distribution)
  median: On output, holds the median of the data
  even: If set and data contains an even number of points,
  medians are computed as the average of the two middle numbers.
  The returned values may not be an element of the original data.

Outputs


  median( |data - median(data)| )

Note


  For the gaussian distribution,
  medabsdev / sigma = inverseErf(0.5) * sqrt(2) = 0.67449

Examples


  IDL> dist = randomn(seed, 50)
  IDL> outlier = 1d7
  IDL> data = [dist, outlier]
  IDL> print, stdev(dist), stdev(data)
      1.09757 1400280.1
  IDL> print, medabsdev(dist), medabsdev(data)
      0.597564 0.59756410

Modification History


  Aug 2009: Written by Chris Beaumont
  Sep 2009: Added /SIGMA keyword. cnb.
  Oct 2009: Added input checking. cnb.
  Oct 2010: Added median keyword. cnb.
  Jul 2012: Added /even keyword. Julio Castro



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