pro ksone, data, func_name, d, prob, xval, \$ PLOT=plot, _EXTRA=extra, Window=window, INTEGER=int, ABOVE=msub, BREAK=ib ;+ ; 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, xval, [ /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. ; xval - data value at which the maximum deviation occurs ; ; 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 xval 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. ; /WINDOW - If set, the plot to a resizeable graphics window ; /INTEGER - Set if func_name is a discrete function taking only integer values ; like the Poisson distribution. ; func_name must be defined down to min(data) - 1 ; If the maximum distance is below the function, xval will return ; one of the data - 1 ; OPTIONAL OUTPUT KEYWORD: ; ABOVE - Returns 0 (false) is the maximum distance is below the expected CDF ; and 1 (true) if it is above ; 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 ; ; A small value of PROB indicates that the cumulative distribution of ; DATA is significantly different from a Gaussian ; ; 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. ; ; Since _EXTRA is used to pass extra parameters both to the user-supplied ; function, and to the cgPLOT command, the user-supplied function should ; not accept "cgPLOT" keyword names (e.g. XTITLE). ; ; PROCEDURE CALLS ; procedure PROB_KS - computes significance of K-S distribution ; TAG_EXIST() ; ; 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 ; Documentation updates W. Landsman June 2003 ; Pass _EXTRA to func_name M. Fitzgerald April, 2005 ; Work for functions that do not accept keywords W. Landsman July 2009 ; Use Coyote graphics for plotting Feb 2011 ; Return xval J. Ballet July 2019 ; Fix plotting, return msub, add DISCRETE option J. Ballet August 2019 ;- On_error, 2 compile_opt idl2 if ( N_params() LT 3 ) then begin print,'Syntax - ksone, data, func_name, D, [prob , xval, /PLOT]' return endif if not keyword_set(int) then int = 0 if not keyword_set(ib) then ib = 0 dsize = SIZE(data) id = dsize[0] if int*dsize[id+1] gt 3 then message, \$ 'ERROR - If INTEGER keyword is set data values must be integer' N = dsize[id+2] if N LT 3 then message, \$ 'ERROR - Input data values (first param) must contain at least 3 values' sortdata = data[ sort( data ) ] if int gt 0 then begin ; Mark duplicates singles = [0,where(sortdata lt sortdata[1:*])+1] ; Create secondary points shifted by 1 from input sortdata = rebin(sortdata,2*N,/sample) ; Do not shift duplicates sortdata[2*singles] -= 1 endif ; We need to determine if the user-supplied function accepts keyword ; arguments. If it does not then passing the _EXTRA keyword will signal ; an error. resolve_routine, func_name,/is_function r = routine_info(func_name,/parameter,/function) if tag_exist(r,'KW_ARGS') then \$ ff = call_function( func_name, sortdata, _EXTRA = extra) else \$ ff = call_function( func_name, sortdata) if int eq 0 then begin sortdata = rebin(sortdata,2*N,/sample) ff = rebin(ff,2*N,/sample) endif f0 = findgen(N)/ N f0 = [0,rebin(f0[1:*],2*(N-1),/sample),1] D = max( abs(f0-ff), sub0 ) xval = sortdata[sub0] msub = f0[sub0] ge ff[sub0] if keyword_set(plot) || keyword_set(WINDOW) then begin ; Slight horizontal offset to avoid overlaying vertical line with CDF eps = 3E-3 * (sortdata[2*N-1]-sortdata[0]) if msub EQ 0 then eps *= -1 cgplot, sortdata, f0,_EXTRA = extra, window=window cgplots, (xval+eps)*[1,1], [0,1], window=window cgplot, /over, sortdata, ff, lines=1, window=window endif PROB_KS, D, N, prob ;Compute significance of K-S statistic if ib gt 0 then stop return end