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Consider the following sequence of random numbers 0.15, 0.94, 0.05, 0.51 and 0.29 has been generated. Use Kolmogorov-Smirnov test to determine whether the hypothesis of uniformity can be rejected

written 10.1 years ago by teamques10 ★ 70k

•   modified 6.1 years ago

given α=0.05 and Critical value D=0.565).

computer simulation and modelling

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written 10.1 years ago by teamques10 ★ 70k

•   modified 10.1 years ago

Step 1)$ H_0: R_i~$ Uniformly (0, 1)

$H_1: R_i~$ is not Uniformly (0, 1)

Step 2) Number of random numbers= N= 5

Step 3) Arrange all random numbers in ascending order

         0.05, 0.15, 0.29, 0.51, 0.94

Step 4)

I	i/N	$R_i$	$i/N-R_i$	i-1	(i-1)/N	$R_i$-((i-1)/N)
1	0.2	0.05	0.15	0	0	0.05
2	0.4	0.15	0.25	1	0.2	-0.05
3	0.6	0.29	0.31	2	0.4	-0.11
4	0.8	0.51	0.29	3	0.6	-0.09
5	1.0	0.94	0.06	4	0.8	0.14

It means that the given samples have property of uniformity.

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