Name

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BIWEIGHT_MEAN

Purpose

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Calculate the center and dispersion (like mean and sigma) of a
distribution using bisquare weighting.

Calling Sequence

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Mean = BIWEIGHT_MEAN( Vector, [ Sigma, Weights ] )

Inputs

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Vector = Distribution in vector form

Output

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Mean - The location of the center.
  OPTIONAL OUTPUT ARGUMENTS:
Sigma = An outlier-resistant measure of the dispersion about the
center, analogous to the standard deviation.
Weights = The weights applied to the data in the last iteration,
                floating point vector

Notes

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      Since a sample mean scaled by sigma/sqrt(N), has a Student's T
      distribution, the half-width of the 95% confidence interval for
      the sample mean can be determined as follows:
          ABS( T_CVF( .975, .7*(N-1) )*SIGMA/SQRT(N) )
      where N = number of points, and 0.975 = 1 - (1 - 0.95)/2.

Procedures Used

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      ROBUST_SIGMA()

Revision History

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Written, H. Freudenreich, STX, 12/89
Modified 2/94, H.T.F.: use a biweighted standard deviation rather than
median absolute deviation.
Modified 2/94, H.T.F.: use the fractional change in SIGMA as the
convergence criterion rather than the change in center/SIGMA.
      Modified May 2002 Use MEDIAN(/EVEN)
      Modified October 2002, Faster computation of weights
      Corrected documentation on 95% confidence interval of mean
                P.Broos/W. Landsman July 2003