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RESISTANT_MEAN

RESISTANT_MEAN

Name


    RESISTANT_Mean

Purpose


    Outlier-resistant determination of the mean and standard deviation.
 

Explanation


    RESISTANT_Mean trims away outliers using the median and the median
    absolute deviation. An approximation formula is used to correct for
    the truncation caused by trimming away outliers

Calling Sequence


    RESISTANT_Mean, ARRAY, Sigma_CUT, Mean, Sigma_Mean, Num_RejECTED
                        [/DOUBLE, DIMENSION= , GOODVEC = ]

Input Argument


      ARRAY = Vector or array to average, NaN values will be ignored
      Sigma_CUT = Data more than this number of standard deviations from the
              median is ignored. Suggested values: 2.0 and up.

Output Argument


      Mean = the mean of the input array, numeric scalar, If the
            DIMENSION keyword is set, then MEAN will be an array with one
            less dimension than the input.

Optional Outputs


Sigma_Mean = the approximate standard deviation of the mean, numeric
            scalar. This is the Sigma of the distribution divided by sqrt(N-1)
            where N is the number of unrejected points. The larger
            SIGMA_CUT, the more accurate. It will tend to underestimate the
            true uncertainty of the mean, and this may become significant for
            cuts of 2.0 or less.
      Num_RejECTED = the number of points trimmed, integer scalar

Optional Input Keywords


      /DOUBLE - If set, then all calculations are performed internally
            in double precision.
      DIMENSION - for a multi-dimensional array, the dimension over which to
            take the mean, starting at 1. If not set, then the scalar mean
            over all elements is used. If this argument is present, the result
            is an array with one less dimension than Array. For example, if
            the dimensions of Array are N1, N2, N3, and Dimension is 2, then
            the dimensions of the result are (N1, N3)
      /SILENT - Set to suppress error messages, e.g.if all values in the array
            are NaN
      SUMDIM - Obsolete synonym for DIMENSION

Optional Output Keyword


      Goodvec - Indices of non-trimmed elements of the input vector
      Wused - synonym for Goodvec (for solarsoft compatibility)

Example


      IDL> a = randomn(seed, 10000) ;Normal distribution with 10000 pts
      IDL> RESISTANT_Mean,a, 3, mean, meansig, num ;3 Sigma clipping
      IDL> print, mean, meansig,num
 
      The mean should be near 0, and meansig should be near 0.01 ( =
        1/sqrt(10000) ).

Procedures Used


      MEAN() - compute simple mean, in Exelis library

Revision History


      Written, H. Freudenreich, STX, 1989; Second iteration added 5/91.
      Use MEDIAN(/EVEN) W. Landsman April 2002
      Correct conditional test, higher order truncation correction formula
                R. Arendt/W. Landsman June 2002
      New truncation formula for sigma H. Freudenriech July 2002
      Divide Sigma_mean by Num_good rather than Npts W. Landsman/A. Conley
                          January 2006
      Use of double precision S. Bianchi February 2008
      More double precision B. Carcich December 2009
      Added DIMENSION keyword (from M. Desnoyer) B. Carcich December 2009
      Use IDL's MEAN() function instead of AVG() W. Landsman Jan 2012
      Use of Dimension keyword yielded transpose of correct value
                    W. Landsman July 2012
      Added NaN keyword to MEAN() call N. Crouzet/WL April 2013
      Allow a row/column to be all NaN values N. Crouzet/WL April 2013
      Use of DIMENSION keyword yielded wrong answer for non-square arrays
                      D. Cottingham December 2014



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