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8: Probability and Statistics Solvers and Properties
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Core Algorithms
Demonstrate the Glivenko-Cantelli Theorem
Demonstrate that the empirical distribution tends to the theoretical distribution as sample size increases by comparing empirical and theoretical CDFs.
In[1]:=
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data = RandomVariate[FrechetDistribution[2, 3, .5], 2500]; lens = {10, 25, 50, 100, 250, 500, 1000, 2500}; edists = Table[EmpiricalDistribution[Take[data, k]], {k, lens}]; limitplot = Plot[CDF[FrechetDistribution[2, 3, .5], x], {x, 0, 20}];
In[2]:=
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GraphicsGrid[ Partition[ Table[Show[ Plot[CDF[edists[[i]], x], {x, 0, 20}, PlotStyle -> Directive[ColorData[1, 2], Thick], PlotRange -> {0, 1}, PlotLabel -> Style[StringJoin["n = ", ToString[lens[[i]]]]]], limitplot], {i, 8}], 2], ImageSize -> 500, Background -> White]
Out[2]=