pro ksone, data, func_name, d, prob, PLOT = plot, _EXTRA = extra
;+
; NAME:
; KSONE
; PURPOSE:
; Compute the one-sided Kolmogorov-Smirnov statistic
; EXPLANATION:
; Returns the Kolmogorov-Smirnov statistic and associated probability for
; for an array of data values and a user-supplied cumulative distribution
; function (CDF) of a single variable. Algorithm from the procedure of
; the same name in "Numerical Recipes" by Press et al. 2nd edition (1992)
;
; CALLING SEQUENCE:
; ksone, data, func_name, D, prob, [ /PLOT ]
;
; INPUT PARAMETERS:
; data - vector of data values, must contain at least 4 elements for the
; K-S 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), though keywords may be
; passed via the _EXTRA facility.
;
; OUTPUT PARAMETERS:
; D - floating scalar giving the Kolmogorov-Smirnov statistic. It
; specified the maximum deviation between the cumulative
; distribution of the data and the supplied function
; prob - floating scalar between 0 and 1 giving the significance level of
; the K-S 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 KSONE will display a
; plot of the CDF of the data with the supplied function
; superposed. The data value where the K-S statistic is
; computed (i.e. at the maximum difference between the data CDF
; and the function) is indicated by a vertical line.
; KSONE accepts the _EXTRA keyword, so that most plot keywords
; (e.g. TITLE, XTITLE, XSTYLE) can also be passed to KSONE.
;
; EXAMPLE:
; Determine if a vector created by the RANDOMN function is really
; consistent with a Gaussian distribution with unit variance.
; 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> ksone, abs(data), 'gauss_cdf', D, prob, /PLOT ;Use K-S test
;
; PROB gives the probability that the null hypothesis (DATA came from a
; Gaussian distribution with unit variance) is correct.
;
; NOTES:
; The code for PROB_KS is from the 2nd (1992) edition of Numerical
; Recipes which includes a more accurate computation of the K-S
; significance for small values of N than the first edition.
;
; PROCEDURE CALLS
; procedure PROB_KS - computes significance of K-S 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
; Converted to IDL V5.0 W. Landsman September 1997
; Documentation updates W. Landsman June 2003
; Pass _EXTRA to func_name M. Fitzgerald April, 2005
;-
On_error, 2
if ( N_params() LT 3 ) then begin
print,'Syntax - ksone, data, func_name, D, [prob ,/PLOT]'
return
endif
N = N_elements( data )
if N LT 3 then message, $
'ERROR - Input data values (first param) must contain at least 3 values'
sortdata = data[ sort( data ) ]
f0 = findgen(N)/ N
fn = ( findgen( N ) +1. ) / N
ff = call_function( func_name, sortdata, _EXTRA = extra)
D = max( [ max( abs(f0-ff), sub0 ), max( abs(fn-ff), subn ) ], msub )
if keyword_set(plot) then begin
if msub EQ 0 then begin
plot, sortdata,f0,psym=10,_EXTRA = extra
plots, [sortdata[sub0], sortdata[sub0]], [0,1]
endif else begin
plot, sortdata,fn,psym=10,_EXTRA = extra
plots, [sortdata[subn], sortdata[subn]], [0,1]
endelse
oplot,sortdata,ff,lines=1
endif
PROB_KS, D, N, prob ;Compute significance of K-S statistic
return
end