New in Wolfram Mathematica 8: Parametric Probability Distributions

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Core Algorithms

Limit Distributions

Some operations, such as sum, min, or max of random variables, converge to only a few limit distributions when repeated. These limit distributions include NormalDistribution, StableDistribution, MinStableDistribution, and MaxStableDistribution, all of which are built into Mathematica 8.

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Grid[Join[{Style[DisplayForm[FormBox[#, TraditionalForm]],

12] & /@ {RowBox[{FractionBox["1",

RowBox[{SqrtBox["n"], " ", "\[Sigma]"}]],

RowBox[{"(",

RowBox[{SubscriptBox["x", "1"], "+", "\[Ellipsis]", "+",

SubscriptBox["x", "n"], "-", RowBox[{"\[Mu]", " ", "n"}]}],

")"}]}],

RowBox[{FractionBox["1",

SuperscriptBox["n", RowBox[{"1", "/", "\[Alpha]"}]]],

RowBox[{"(",

RowBox[{SubscriptBox["x", "1"], "+", "\[Ellipsis]", "+",

SubscriptBox["x", "n"]}], ")"}]}],

RowBox[{RowBox[{SubscriptBox["a", "n"], " ",

RowBox[{"max", "(",

RowBox[{SubscriptBox["x", "1"], ",", "\[Ellipsis]", ",",

SubscriptBox["x", "n"]}], ")"}]}], "+",

SubscriptBox["b", "n"]}]}}, {clt, gclt, max} //

Transpose, {Style[#, 14, Bold,

FontFamily -> "Helvetica"] & /@ {NormalDistribution,

StableDistribution, MaxStableDistribution}}],

Dividers -> {{False, True, True, False}, {False, True, True, True,

False, {False}}}, FrameStyle -> LightGray]

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