Use the Kolmogorov-Smirnov Test to determine if numbers are uniformly distributed on given interval.

From Probability Concepts and Random Number Generation chapter in PU/ Simulation and Modelling

Asked by arjun adhikari on 13 Apr, 2022

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The following numbers have been generated

0.44, 0.19, 0.88, 0.27, 0.55, 0.13, 0.63, 0.74, 0.11 and 0.33.


Use the Kolmogorov-Smirnov Test with a=0.05 to determine, if the hypothes is that the numbers are uniformly distributed on interval [0, 1] can be rejected. Use the critical value of D for a =0.05 and N=10 is 0.410 

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Alson Garbuja on 14 Apr, 2022 Like 1 Dislike

We have,

n = 10

Ri 0.11 0.13 0.19 0.27 0.33 0.44 0.55 0.63 0.74 0.88
(i/n - Ri) -0.01 0.07 0.11 0.13 0.17 0.16 0.15 0.17 0.16 0.12
(Ri - (i-1)/n) 0.11 0.03 -0.01 -0.03 -0.07 -0.06 -0.05 -0.07 -0.06 -0.02

 

Then, 

D+ = MAX{i/n - Ri} = 0.17

D- = MAX{Ri - (i-1)/n} = 0.03

 

D = MAX(D+, D-) = 0.17

Since D < Da hence the hypothesis is accpeted

comments on the answer (1)

Like 0 Dislike D- ko max 0.11 hunxa, aru tah same hunxa Alson Garbuja on 28 May, 2022

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