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KUIPERONE

KUIPERONE

## Purpose

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

## Explanation

Returns the Kuiper statistic and associated probability
for an array of data values and a user-supplied cumulative distribution
function (CDF) of a single variable. Algorithm adapted from KSONE
in "Numerical Recipes" by Press et al. 2nd edition (1992)
Kuiper's test is especially useful for data defined on a circle or
to search for periodicity (see Paltani 2004, A&A, 420, 789).

## Calling Sequence

kuiperone, data, func_name, D, prob, [ /PLOT ]

## Input Parameters

data - vector of data values, must contain at least 4 elements for the
Kuiper statistic to be meaningful
func_name - scalar string giving the name of the cumulative distribution
function. The function must be defined to accept the data
vector as its only input (see example).

## Output Parameters

D - floating scalar giving the Kuiper statistic. It
specifies the sum of positive and negative deviations between the
cumulative distribution of the data and the supplied function
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 DATA is significantly
different from FUNC_NAME.

## Optional Input Keyword

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

## Example

Determine if a vector created by the RANDOMN function is really
consistent with a Gaussian distribution.
The CDF of a Gaussian is the error function except that a factor
of 2 is included in the error function. So we must create a special
function:
function gauss_cdf, x
return, errorf( x/sqrt(2) )
end
IDL> data = randomn(seed, 50) ;create data array to be tested
IDL> kuiperone, data, 'gauss_pdf', D, prob, /PLOT ;Use Kuiper test
A small value of PROB indicates that the cumulative distribution of
DATA is significantly different from a Gaussian

## Notes

Note that the 2nd (1992) edition of Numerical Recipes includes
a more accurate computation of the K-S significance for small
values of N.

## Procedure Calls

procedure PROB_KUIPER - computes significance of Kuiper distribution

## Revision History

Written W. Landsman August, 1992
Accept _EXTRA keywords W. Landsman September, 1995
Fixed possible bug in plot display showing position maximum difference
in histogram M. Fardal/ W. Landsman March, 1997
Adapted from KSONE J. Ballet July 2003
Use Coyote graphics W. Landsman Feb 2011

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