Samples generations using discrete probability and Kolmogorov-Sirmnov test
Example. A Discrete Poisson sample of size 1000 with parameter lambda=5 :
TestSamplesPoisson(1000, 5.0);
Will produce
data={5,10,4,7,7,2,1,3,6,2,6,3,1,3,4,9,5,4,4,7,1,6,7,1,5,1,6,9,6,4,4,6,10,4,3,9,7,4,3,7,5,4,2,3,3,6,2,4,4,6,4,8,4,8,4,7,3,4,4,7,5,2,5,4,7,1,3,6,1,5,3,2,3,6,4,6,5,6,7,7,8,4,6,9,9,4,4,2,2,4,7,4,3,4,4,4,7,6,4,3,5,5,4,7,5,4,6,6,5,5,4,5,5,5,8,3,4,5,4,4,6,2,5,6,5,6,9,7,4,9,7,7,4,5,4,4,12,7,4,6,6,6,5,5,2,4,7,6,4,3,9,4,4,9,5,4,9,6,3,8,4,7,4,5,7,5,2,2,2,5,3,5,2,7,6,10,6,2,6,3,8,3,5,3,14,5,5,4,10,10,5,4,6,5,4,7,4,8,6,5,4,7,6,8,0,4,3,5,3,5,6,8,0,11,10,2,4,3,5,4,9,6,2,2,12,7,9,6,5,7,6,6,4,2,9,2,6,5,3,5,3,9,3,4,3,5,4,6,5,3,5,2,3,4,6,5,6,5,9,3,5,6,2,4,9,15,5,9,1,8,5,8,2,1,2,11,5,6,7,4,5,4,2,3,4,5,5,8,4,4,4,2,5,8,3,5,7,6,5,3,1,4,5,6,6,5,10,3,4,6,9,2,6,5,6,3,5,8,1,4,5,6,5,6,5,4,4,3,7,5,3,8,3,6,4,2,6,5,5,7,5,3,5,7,5,4,4,2,3,0,2,9,6,2,6,4,8,10,3,4,4,7,4,8,5,2,7,1,3,6,4,2,4,3,7,3,2,6,3,3,9,3,13,7,4,3,3,3,8,12,3,6,4,2,5,7,8,6,4,4,5,4,8,5,5,1,5,5,4,5,4,3,7,10,4,2,7,5,5,4,8,6,3,3,5,6,7,4,6,10,4,4,4,6,6,5,4,5,4,4,6,6,7,4,6,0,8,4,6,4,11,4,3,11,5,7,4,7,8,8,3,3,6,4,3,8,6,2,4,7,7,3,3,3,6,4,7,6,5,5,7,5,6,4,10,11,4,4,3,7,4,5,6,4,2,4,8,5,4,7,3,7,0,7,5,6,3,9,4,3,11,5,4,4,2,7,6,4,4,3,6,4,7,5,5,4,6,7,2,4,4,4,4,6,4,9,4,7,7,3,7,4,3,0,7,6,3,4,4,4,6,5,2,3,3,8,11,5,3,4,2,4,8,9,8,5,2,6,2,3,4,7,5,3,4,4,3,7,6,7,2,4,5,6,5,7,4,4,5,4,9,9,5,5,3,5,5,3,3,3,5,5,3,3,10,8,1,9,7,7,6,3,7,4,3,6,8,3,4,2,4,7,2,6,3,4,4,1,10,7,7,1,6,5,3,5,3,4,7,6,7,4,5,6,6,7,3,3,4,4,5,4,7,2,8,7,5,5,9,5,5,11,11,13,11,6,4,4,3,7,5,5,4,7,4,10,4,4,2,4,3,3,6,5,3,5,3,6,6,5,9,6,4,3,1,7,4,5,6,8,4,8,10,5,7,2,9,0,6,8,5,3,4,5,4,4,3,4,7,5,5,7,6,6,7,9,3,3,6,5,6,7,6,3,2,4,3,3,7,3,5,3,8,6,0,7,3,7,7,5,5,8,6,4,5,5,3,4,6,7,8,7,3,3,3,5,5,4,5,1,3,11,6,6,8,3,8,9,6,1,6,4,4,3,9,6,3,4,6,5,2,8,5,8,3,7,10,6,5,4,4,9,4,7,4,5,4,2,4,3,6,4,5,6,3,5,5,2,4,5,5,3,5,10,11,4,4,6,4,2,3,3,5,4,7,6,8,5,7,4,5,2,9,5,7,6,4,9,7,6,4,8,4,8,9,2,4,4,7,1,3,5,6,4,9,5,7,4,7,4,6,1,4,8,2,4,3,2,3,4,1,5,9,6,7,4,7,5,4,6,4,5,6,7,3,8,4,6,5,4,8,10,2,4,0,4,5,5,7,5,8,4,3,5,1,6,5,1,5,5,6,4,9,3,1,3,4,5,6,3,1,5,5,8,4,2,4,5,6,5,7,4,6,7,6,1,4,2,6,5,4,4,2,9,6,6,1,8,4,7,8,1,7,6,5,4,7,4,3,9,4,13,4,1,7,3,5,3,5,1,7,4,7,2,7,6,5,5,3,7,1,4,3,7,6,6,5,2,4,4};
Histogram[data,{1}]
ProbabilityPlot[data,PoissonDistribution[5]]
DistributionFitTest[data,PoissonDistribution[5],{"TestStatisticTable", "KolmogorovSmirnov"}]
Print["Discrete KolmogorovSmirnov:0.027025915 Test:0.043007 => Accepted alpha=0.05"]
The Mathematica code above can be tested online at https://develop.wolframcloud.com The computed value of KolmokorovSmirnov test by Mathematica is exactly the same.
