‹›拡張された確率と統計の機能変換された分布の自動簡約機能の向上
バージョン11では,変換された分布用の自動簡約規則がさらに加えられた.
一様分布に従う確率変数のベキは,ベータ分布に従う.
TransformedDistribution[X^a, X \[Distributed] UniformDistribution[]]
独立指数分布に従う確率変数の比は,パレート(Pareto)分布を満足する.
TransformedDistribution[
X/Y, {X \[Distributed] ExponentialDistribution[b],
Y \[Distributed] ExponentialDistribution[a]}]
正規分布に従う確率変数の逆数の平方は,レヴィ(Lévy)分布に従う.
TransformedDistribution[X^(-2),
X \[Distributed] NormalDistribution[0, s]]
その他の例.
完全なWolfram言語入力を表示する
SetAttributes[fun, HoldFirst];
fun[x_] := {HoldForm[x], x};
Grid[Map[Style[#, ScriptLevel -> 0] &,
Join[{{"Transformed Distribution", "Simplified Distribution"}}, {
fun[TransformedDistribution[
Min[Subscript[X, 1], Subscript[X,
2]], {Subscript[X, 1] \[Distributed]
BernoulliDistribution[Subscript[p, 1]],
Subscript[X, 2] \[Distributed]
BernoulliDistribution[Subscript[p, 2]]}]],
fun[TransformedDistribution[1/X,
X \[Distributed] LogLogisticDistribution[\[Gamma], \[Sigma]]]],
fun[TransformedDistribution[k*X,
X \[Distributed] ChiDistribution[\[Nu]]]],
fun[TransformedDistribution[1/X,
X \[Distributed] BetaPrimeDistribution[a, b]]],
fun[TransformedDistribution[k*Exp[-X],
X \[Distributed] ExponentialDistribution[a]]],
fun[TransformedDistribution[-Log[X],
X \[Distributed] PowerDistribution[1, a]]],
fun[TransformedDistribution[c*X,
X \[Distributed] ChiSquareDistribution[a]]],
fun[TransformedDistribution[1 + X,
X \[Distributed] ExponentialDistribution[a]]],
fun[TransformedDistribution[
Sqrt[X*Y], {X \[Distributed] ExponentialDistribution[m],
Y \[Distributed] GammaDistribution[a, b]}]],
fun[TransformedDistribution[Log[X]/2,
X \[Distributed] FRatioDistribution[n, m]]],
fun[TransformedDistribution[R^2,
R \[Distributed] RiceDistribution[\[Nu], 1]]]
}], {2}], Dividers -> All, Spacings -> {4, 2},
Background -> {None, {{None, GrayLevel[.9]}}, {{1, 1} ->
Hue[.6, .4, 1], {1, 2} -> Hue[.6, .4, 1]}},
BaseStyle -> {FontFamily -> Times, FontSize -> 13},
Alignment -> {Center, Center}] // TraditionalForm