14.3 Are Two Distributions Different? 625 where Ne is the effective number of data points,Ne =N for the case (14.3.5) of one distribution,and Ne= NiN2 (14.3.10) N1+N2 for the case(14.3.6)of two distributions,where Ni is the number of data points in the first distribution,N2 the number in the second. The nature of the approximation involved in(14.3.9)is that it becomes asymp- totically accurate as the Ne becomes large,but is already quite good for Ne >4,as small a number as one might ever actually use.(See [1].) 81 So,we have the following routines for the cases of one and two distributions: 鱼a #include <math.h> #include "nrutil.h" void ksone(float data[],unsigned long n,float (*func)(float),float *d, float tprob) Given an array data [1..n],and given a user-supplied function of a single variable func which RECIPES is a cumulative distribution function ranging from 0 (for smallest values of its argument)to 1 (for largest values of its argument),this routine returns the K-S statistic d,and the significance 令 level prob.Small values of prob show that the cumulative distribution function of data is significantly different from func.The array data is modified by being sorted into ascending order. Press. float probks(float alam); void sort(unsigned long n,float arr[]); unsigned long j; float dt,en,ff,fn,fo=0.0; sort(n,data); If the data are already sorted into as- IENTIFIC en=n; cending order,then this call can be *d=0.0; omitted. for (j=1;j<=n;j++) Loop over the sorted data points. fn=j/en; Data's c.d.f.after this step. COMPUTING ff=(*func)(data[j]) Compare to the user-supplied function. dt=FMAX(fabs(fo-ff),fabs(fn-ff)); Maximum distance. 1920 if (dt>*d)*d=dt; (ISBN fo=fn; en=sqrt(en); *prob=probks((en+0.12+0.11/en)*(*d)); Compute significance. Numerical Recipes 431086 (outside #include <math.h> Software. void kstwo(float datai[],unsigned long ni,float data2[],unsigned long n2, float *d,float *prob) Given an array data1[1..n1],and an array data2[1..n2],this routine returns the K- S statistic d,and the significance level prob for the null hypothesis that the data sets are drawn from the same distribution.Small values of prob show that the cumulative distribution function of data1 is significantly different from that of data2.The arrays datal and data2 are modified by being sorted into ascending order. float probks(float alam); void sort(unsigned long n,float arr); unsigned long j1=1,j2=1; float d1,d2,dt,en1,en2,en,fn1=0.0,fn2=0.0;14.3 Are Two Distributions Different? 625 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). where Ne is the effective number of data points, Ne = N for the case (14.3.5) of one distribution, and Ne = N1N2 N1 + N2 (14.3.10) for the case (14.3.6) of two distributions, where N1 is the number of data points in the first distribution, N2 the number in the second. The nature of the approximation involved in (14.3.9) is that it becomes asymp￾totically accurate as the Ne becomes large, but is already quite good for Ne ≥ 4, as small a number as one might ever actually use. (See [1].) So, we have the following routines for the cases of one and two distributions: #include <math.h> #include "nrutil.h" void ksone(float data[], unsigned long n, float (*func)(float), float *d, float *prob) Given an array data[1..n], and given a user-supplied function of a single variable func which is a cumulative distribution function ranging from 0 (for smallest values of its argument) to 1 (for largest values of its argument), this routine returns the K–S statistic d, and the significance level prob. Small values of prob showthat the cumulative distribution function of data is significantly different from func. The array data is modified by being sorted into ascending order. { float probks(float alam); void sort(unsigned long n, float arr[]); unsigned long j; float dt,en,ff,fn,fo=0.0; sort(n,data); If the data are already sorted into as￾cending order, then this call can be omitted. en=n; *d=0.0; for (j=1;j<=n;j++) { Loop over the sorted data points. fn=j/en; Data’s c.d.f. after this step. ff=(*func)(data[j]); Compare to the user-supplied function. dt=FMAX(fabs(fo-ff),fabs(fn-ff)); Maximum distance. if (dt > *d) *d=dt; fo=fn; } en=sqrt(en); *prob=probks((en+0.12+0.11/en)*(*d)); Compute significance. } #include <math.h> void kstwo(float data1[], unsigned long n1, float data2[], unsigned long n2, float *d, float *prob) Given an array data1[1..n1], and an array data2[1..n2], this routine returns the K– S statistic d, and the significance level prob for the null hypothesis that the data sets are drawn from the same distribution. Small values of prob showthat the cumulative distribution function of data1 is significantly different from that of data2. The arrays data1 and data2 are modified by being sorted into ascending order. { float probks(float alam); void sort(unsigned long n, float arr[]); unsigned long j1=1,j2=1; float d1,d2,dt,en1,en2,en,fn1=0.0,fn2=0.0;