Name

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      KUIPERTWO

Purpose

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      Compute the two-sided Kuiper statistic (invariant Kolmogorov-Smirnov)

Explanation

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      Returns the Kuiper statistic and associated probability
      that two arrays of data values are drawn from the same distribution
      Algorithm adapted from KSTWO in "Numerical
      Recipes" by Press et al., 2nd edition (1992), Chapter 14

Calling Sequence

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      kuipertwo, data1, data2, D, prob, [ /PLOT ]

Input Parameters

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      data1 - vector of data values, at least 4 data values must be included
              for the Kuiper statistic to be meaningful
      data2 - second set of data values, does not need to have the same
              number of elements as data1

Output Parameters

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      D - floating scalar giving the Kuiper statistic. It
              specifies the sum of positive and negative deviations between
              the cumulative distributions of the two data sets
      prob - floating scalar between 0 and 1 giving the significance level of
              the Kuiper statistic. Small values of PROB show that the
              cumulative distribution function of DATA1 is significantly
              different from DATA2

Optional Input Keyword

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      /PLOT - If this keyword is set and non-zero, then KUIPERTWO will display
              a plot of the CDF of the two data sets.
              The data values where the Kuiper statistic is
              computed (i.e. at the maximum difference between the CDF of
              the two data sets) are indicated by vertical dashed lines.
              KUIPERTWO accepts the _EXTRA keyword, so that most plot keywords
              (e.g. TITLE, XTITLE, XSTYLE) can also be passed to KUIPERTWO.
      /WINDOW - If set the plot to a resizeable graphics window.

Example

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      Test whether two vectors created by the RANDOMN function likely came
      from the same distribution
      IDL> data1 = randomn(seed,40) ;Create data vectors to be
      IDL> data2 = randomn(seed,70) ;compared
      IDL> kuipertwo, data1, data2, D, prob & print,D,prob

Procedure Calls

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      procedure PROB_KUIPER - computes significance of Kuiper distribution

Revision History

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      Written W. Landsman August, 1992
      FP computation of N_eff H. Ebeling/W. Landsman March 1996
      Fix for arrays containing equal values J. Ballet/W. Landsman
      Oct. 2001
      Adapted from KSTWO, added PLOT keyword J. Ballet July 2004
      Use Coyote Graphics W. Landsman Feb 2011