# ks - Kolmogorov-Smirnov Test Steps Hypothesis Sampling Test...

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Kolmogorov-Smirnov Test

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Steps Hypothesis Sampling Test
Hypothesis Given data: x 1 ,...,x n Draw a Histogram and guess distribution F. Draw an Ecdf, G, and compute d. - G(x)=sum(I(x i <x))/n - d=max(|G(x i )-F(x i )|,|F(x i )-G(x i-1 )|) for all i.

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Sampling Use computer to build data having distribution F: y 1 ,...,y n Draw an Ecdf, G, and compute d 1 . - G(x)=sum(I(y i <y))/n - d 1 =max(|G(y i )-F(y i )|,|F(y i )-G(y i-1 )|) for all i. Repeat m times so that you have d 1 ,...,d m
Test Compare d to the d i 's using a relative frequence probability; - Pvalue = sum(d>d i )/m

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Example. .. What distribution do you think the following data comes from? 0.52 0.98 3.69 4.11 0.27 2.37 2.63 1.96 2.92 1.17 1.19 3.41 0.84 1.96 3.95 0.96 2.83 1.22 2.02 1.11 1.62 0.34 5.66 2.66 0.66 6.22 0.53 0.77 1.71 0.85
Possibilities A) Exponential B) Chi Squared C) Gamma D) A or B E) A or B or C

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data=c(0.52, 0.98, 3.69, 4.11, 0.27, 2.37, 2.63, 1.96, 2.92, 1.17, 1.19, 3.41, 0.84, 1.96,
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ks - Kolmogorov-Smirnov Test Steps Hypothesis Sampling Test...

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