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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>trimmean</TITLE>
  <TYPE>  </TYPE>
  <DATE>October 2002</DATE>
  <SHORT_DESCRIPTION name="trimmean"> trimmed mean of a vector or a matrix</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>m=trimmean(x)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>m=trimmean(x,discard,'r') or m=trimmean(x,discard,1)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>m=trimmean(x,discard,'c') or m=trimmean(x,discard,2)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>x</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>real or complex vector or matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>discard</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>number: The discarding percentage</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    A  trimmed mean  is calculated  by discarding  a certain
    percentage of the lowest and the highest scores and then
    computing  the  mean   of  the  remaining  scores.   For
    example, a  mean trimmed  50% is computed  by discarding
    the lower  and higher 25%  of the scores and  taking the
    mean of the remaining scores.</P>
    <P>
    The median  is the mean trimmed 100%  and the arithmetic
    mean is the mean trimmed 0%.</P>
    <P>
    A  trimmed mean  is  obviously less  susceptible to  the
    effects of  extreme scores than is  the arithmetic mean.
    It is therefore less susceptible to sampling fluctuation
    than the mean for  extremely skewed distributions. It is
    less  efficient (The  efficiency of  a statistic  is the
    degree to  which the statistic is stable  from sample to
    sample.    That  is,  the   less  subject   to  sampling
    fluctuation  a  statistic  is,  the  more  efficient  it
    is. The efficiency of statistics is measured relative to
    the  efficiency  of other  statistics  and is  therefore
    often called the relative efficiency. If statistic A has
    a  smaller   standard  error  than   statistic  B,  then
    statistic  A is  more efficient  than statistic  B.  The
    relative efficiency of two  statistics may depend on the
    distribution involved.   For instance, the  mean is more
    efficient than  the median for  normal distributions but
    not  for  some   extremely  skewed  distributions.   The
    efficiency of a statistic can  also be thought of as the
    precision  of  the  estimate:  The  more  efficient  the
    statistic,  the  more precise  the  statistic  is as  an
    estimator         of         the         parameter.[from
    http://davidmlane.com/hyperstat/A12977.html])  than  the
    mean for normal distributions.</P>
    <P>
    Trimmed  means  are often  used  in  Olympic scoring  to
    minimize the effects  of extreme ratings possibly caused
    by            biased            judges.            [from
    http://davidmlane.com/hyperstat/A11971.html]</P>
    <P>
    For      a      vector      or     matrix      <VERB>x</VERB>,
    <VERB>t=trimmean(x,discard)</VERB>  returns in  scalar <VERB>t</VERB>
    the  mean   of  all  the  entries   of  <VERB>x</VERB>,  after
    discarding    <VERB>discard/2</VERB>   highest    values   and
    <VERB>discard/2</VERB> lowest values.</P>
    <P><VERB>t=trimmean(x,discard,'r')</VERB>    (or,   equivalently,
    <VERB>t=trimmean(x,discard,1)</VERB>) returns in each entry of
    the row vector <VERB>t</VERB>  the trimmed mean of each column
    of <VERB>x</VERB>.</P>
    <P><VERB>t=trimmean(x,discard,'c')</VERB>    (or,   equivalently,
    <VERB>t=trimmean(x,discard,2)</VERB>) returns in each entry of
    the column vector <VERB>t</VERB>  the trimmed mean of each row
    of <VERB>x</VERB>.</P>
    <P>
    This function computes the  trimmed mean of a vector or
    matrix <VERB> x</VERB>.</P>
    <P>
    For a vector or matrix <VERB> x</VERB>, <VERB> m=trimmean(x) </VERB>
    returns in scalar <VERB> m</VERB> the trimmedmean of all the
    entries of <VERB> x</VERB>.</P>
    <P><VERB>   m=trimmean(x,'r')  </VERB>  (or,   equivalently,  <VERB>
    m=trimmean(x,1) </VERB>)  returns in each entry  of the row
    vector <VERB> m</VERB> the trimmed mean of each column of <VERB>
    x</VERB>.</P>
    <P>
    q<VERB>  m=trimmean(x,'c')   </VERB>  (or,  equivalently,  <VERB>
    m=trimmean(x,2)  </VERB>)  returns  in  each entry  of  the
    column vector <VERB> m</VERB> the trimmed mean of each row of
    <VERB> x</VERB>.</P>
  </DESCRIPTION>
  <SECTION label="References">
    <P>
     Luis  Angel   Garcia-Escudero  and  Alfonso  Gordaliza, Robustness Properties of Means and Trimmed Means, JASA, Volume 94, Number 447, Sept 1999, pp956-969</P>
  </SECTION>
  <AUTHOR> Carlos Klimann</AUTHOR>
</MAN>
