Name

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  MPCHILIM

Author

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  Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
  craigm@lheamail.gsfc.nasa.gov
  UPDATED VERSIONs can be found on my WEB PAGE:
      http://cow.physics.wisc.edu/~craigm/idl/idl.html

Purpose

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  Compute confidence limits for chi-square statistic

Major Topics

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  Curve and Surface Fitting, Statistics

Calling Sequence

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  DELCHI = MPCHILIM(PROB, DOF, [/SIGMA, /CLEVEL, /SLEVEL ])

Description

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  The function MPCHILIM() computes confidence limits of the
  chi-square statistic for a desired probability level. The returned
  values, DELCHI, are the limiting chi-squared values: a chi-squared
  value of greater than DELCHI will occur by chance with probability
  PROB:
    P_CHI(CHI > DELCHI; DOF) = PROB
  In specifying the probability level the user has three choices:
    * give the confidence level (default);
    * give the significance level (i.e., 1 - confidence level) and
      pass the /SLEVEL keyword; OR
    * give the "sigma" of the probability (i.e., compute the
      probability based on the normal distribution) and pass the
      /SIGMA keyword.
  Note that /SLEVEL, /CLEVEL and /SIGMA are mutually exclusive.

Inputs

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  PROB - scalar or vector number, giving the desired probability
          level as described above.
  DOF - scalar or vector number, giving the number of degrees of
        freedom in the chi-square distribution.

Returns

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  Returns a scalar or vector of chi-square confidence limits.

Keyword Parameters

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  SLEVEL - if set, then PROB describes the significance level.
  CLEVEL - if set, then PROB describes the confidence level
            (default).
  SIGMA - if set, then PROB is the number of "sigma" away from the
          mean in the normal distribution.

Examples

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  print, mpchilim(0.99d, 2d, /clevel)
  Print the 99% confidence limit for a chi-squared of 2 degrees of
  freedom.
  print, mpchilim(5d, 2d, /sigma)
  Print the "5 sigma" confidence limit for a chi-squared of 2
  degrees of freedom. Here "5 sigma" indicates the gaussian
  probability of a 5 sigma event or greater.
      P_GAUSS(5D) = 1D - 5.7330314e-07

References

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  Algorithms taken from CEPHES special function library, by Stephen
  Moshier. (http://www.netlib.org/cephes/)

Modification History

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  Completed, 1999, CM
  Documented, 16 Nov 2001, CM
  Reduced obtrusiveness of common block and math error handling, 18
    Nov 2001, CM
  Convert to IDL 5 array syntax (!), 16 Jul 2006, CM
  Move STRICTARR compile option inside each function/procedure, 9
    Oct 2006
  Add usage message, 24 Nov 2006, CM
  Usage message with /CONTINUE, 23 Sep 2009, CM