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8: Parametric Probability Distributions
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Core Algorithms
Univariate Discrete Distributions
Discrete univariate parametric distributions in
Mathematica
8.
In[1]:=
X
dists = {BenfordDistribution[10], BernoulliDistribution[0.3], BetaBinomialDistribution[2, 3, 20], BetaNegativeBinomialDistribution[6, 4, 20], BinomialDistribution[20, .6], BorelTannerDistribution[.3, 10], DiscreteUniformDistribution[{1, 20}], FisherHypergeometricDistribution[25, 13, 52, 2], GeometricDistribution[.4], HypergeometricDistribution[30, 40, 80], LogSeriesDistribution[.4], NegativeBinomialDistribution[10, .3], PascalDistribution[2, .3], PoissonDistribution[9], PoissonConsulDistribution[9, .3], PolyaAeppliDistribution[4, .5], SkellamDistribution[12, 3], WalleniusHypergeometricDistribution[13, 13, 52, 2], WaringYuleDistribution[1.4], WaringYuleDistribution[3, 16], ZipfDistribution[1.2], ZipfDistribution[10, .2]};
In[2]:=
X
plots = ParallelTable[ DiscretePlot[PDF[d, x], {x, Quantile[d, 0.05], Quantile[d, 0.95]}, PlotRange -> All, ExtentSize -> 1/2, Ticks -> None, FillingStyle -> Directive[Opacity[1], RandomChoice[ColorData[45, "ColorList"]]], BaseStyle -> Opacity[1], PlotLabel -> StringReplace[ToString[Head[d]], "Distribution" -> ""]], {d, dists}];
In[3]:=
X
composite = Table[Hyperlink[ Tooltip[Show[plots[[i]], ImageSize -> 125], Show[plots[[i]], PlotLabel -> dists[[i]], ImageSize -> Large, Ticks -> Automatic]], "paclet:ref/" <> ToString[Head[dists[[i]]]]], {i, Length[dists]}];
In[4]:=
X
Grid[Partition[Join[composite, {Null, Null}], 4]]
Out[4]=