Downloaded from https://www.everyspec.com AMCP 706. 93 TABLE 2.13 RANDOM $AMPLE FROM THE UNIFORM DISTRIBUTION These numbers were taken from a table of pseudo-random number* which were uniformly distributed between 0.00 and 1,00. They have been ordered from smallest to largest. N (sample size) 20; r Is the order number; Y Is the random variable, r X r N ' N 1 0,01 a 0.24 11 0.57 16 0.84 2 0.02 7 0,48 12 0.65 17 0.66 3 0,03 8 0Q48 13 0.70 1811 0.87 4 0.08 9 (1.52 14 0.75 19 0,88 5 0.23 10 0.57 15 0.79 20 0.99 The sample Cdf and the 95% o-confidence limits (ase Table 2-12) are plotted In Fig, 2.121A). Each point In the tablu is plotted at Jr-l 1/N and at OIN for the sample Cdf.
It is easy to see that the sample could easily If Fhyp, Wx Is to be rejected by crossing have come from many other distributions, line L (see path A), the earliest It can do so I.e., any that Ilie between lines U and L. Is for' the smallest sample-point number iA for which In practice, plotting the graphs will be In (iA/N) -.
d ?2F4 k) (- accurate and/or tedious for N > 10, sny, 2-6 T'herefore, the shortcut analytic method (des- Ti ss eas d a ee erae cribed in the next paragraph) ought to be Ti ss eas d a ee erae used, It Is based on the fact that, even at If Fhvp (x) Is to be rejected by crossing poor (low) levels of s-confidence the critical line U (see path B), the earliest It can do so value of d is large compared to I/IN (I/IN Is is for the smallest sample-point number I, the increase In the sample ('df at each sample for which * point). At each "evaluated sample-point" It is reasonably easy to calculate the smallest , subsequent sample-paint which could pos.
F by 0 X q i) -- (1 0 /IN ) d (2-47) sibly cause rejection of the hypothetical dis- This is so because the sample Cdf increase tribution. by I/IN at each sample point. F~ig, 2-1 2(8) shows hOW this exercise is The next sample-point number is the done. Suppose the sample-point number i smaller of 1A and ifi, Example No. I1111- * i,, has been evaluated and Is within the lines lustrates the procedure. U and L as described in Fig, 2-12(A). Fig. * 2-1 2(b) is a small portion of a typical sample 2-5 KOLMOGOROV-8MIRNOV euCONPI- C'df plot with the K-S lines U and L sh~own DENCE LIMITS on it. F~y(x) can be rejected only itf it crosses lines U or L, wewill find the small- C~hapter 30 of Ref.
24 (and other Wrefr est sample-point for which that can happen. ences) shows that the K-S critical values in 2-71 ~