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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
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)
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

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