Core Algorithms

Prepare a Table of Special Transformations

Prepare a table of special transformations of random variables that lead to built-in parametric distributions.

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specialtransformations = {HoldForm[

TransformedDistribution[a x + b,

x \[Distributed] NormalDistribution[\[Mu], \[Sigma]]]],

HoldForm[

TransformedDistribution[Sqrt[x],

x \[Distributed] ExponentialDistribution[1]]],

HoldForm[

TransformedDistribution[x^2,

x \[Distributed] StudentTDistribution[\[Nu]]]],

HoldForm[

TransformedDistribution[

Sqrt[x^2 + y^2], {x, y} \[Distributed]

BinormalDistribution[{a, b}, {c, d}, e]]],

HoldForm[

TransformedDistribution[Tan[x],

x \[Distributed] UniformDistribution[{-Pi/2, Pi/2}]]],

HoldForm[

TransformedDistribution[

x + y + z, {x, y, z} \[Distributed]

ProductDistribution[{PoissonDistribution[\[Mu]], 3}]]],

HoldForm[

TransformedDistribution[

Min[x, y], {x \[Distributed]

GeometricDistribution[Subscript[p, 1]],

y \[Distributed] GeometricDistribution[Subscript[p, 2]]}]],

HoldForm[

TransformedDistribution[

x - y, {x \[Distributed]

PoissonDistribution[Subscript[\[Mu], 1]],

y \[Distributed] PoissonDistribution[Subscript[\[Mu], 2]]}]],

HoldForm[

TransformedDistribution[Exp[u],

u \[Distributed] NormalDistribution[\[Mu], \[Sigma]]]]};

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