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Harris Geospatial / Docs Center / Libraries / Beaumont / EDF_STATS

EDF_STATS

EDF_STATS

Purpose


  This function calculates a variety of statistics to characterize
  the discrepancy between 1D data and a model for the distribution
  from which the data were drawn. Each statistic is based on the
  empirical distribution function (i.e. the cdf of the data). Such
  statistics can be used to evaluate whether a model distribution is
  consistent with the data.
  In what follows, Fn(x) is the empirical distribution function (edf)
  and F(x) is the model cdf. Currently, four statistics are
  implemented:
  1) The Kolmogorov-Smirnov Statistic: max(|F(x) - Fn(x)|)
  2) An Anderson-Darling style statistic:
      Mean( (Fn(x) - F(x))^2 / (F(x) * (1 - F(x))) )
  3) The Kuyper Statistic: max(F(x) - Fn(x)) + max(Fn(x) - F(x))
  4) The mean absolute deviation:
      Mean( |Fn(x) - F(x)| )
  Note that statistic 2 is designed to be more sensitive to
  discrepancies at low and high values of x than is the KS stat
  Note also that the Kuyper statistic is meant to be used for values
  of x wrapped onto a circle. See Numerical Recipes.

Category


  Statistics

Calling Sequence


  result = edf_stats(data, model, [ks = ks, ad = ad, ky = ky, mad = mad])
        or
  result = edf_stats(data, model, [/ks or /ad or /ky, /mad])

Inputs


  data: A vector of data values
  model: The string name of a function which calculates the cdf of
        the model distribution. The function must have the calling
        sequence result = model(x, _extra = extra), and must be
        written to handle x as a scalar or vector. Extra keywords to
        edf_stats will be passed to this function.
 

Keyword Parameters


  ks: If non zero or set to a named variable, will calculate and
  return the ks statistic to that variable.
 
  ad: Same as above, for the Anderson-Darling statistic.
  ky: Same as above, for the Kuyper statistic
  mad: Same as above, for the mediat absolute deviation

Outputs


  If only one of ks, ad, ky, or mad are set, then the return value is
  that particular statistic. Otherwise, the KS statistic is returned.

See Also


  edf

Modification History


  June 2009: Written by Chris Beaumont
  July 2009: Added mad statistic



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