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MPCHILIM

MPCHILIM

## Author

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

Compute confidence limits for chi-square statistic

## Major Topics

Curve and Surface Fitting, Statistics

## Calling Sequence

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

## Description

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

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

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

## Keyword Parameters

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

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

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

## Modification History

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
\$Id: mpchilim.pro,v 1.8 2009/09/23 20:12:46 craigm Exp \$

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