DirichletDistribution
متاحة
Dirichlet distribution over the probability simplex (Mean/Variance/Covariance/StandardDeviation/PDF)
DirichletDistribution[{α 1, …, α k + 1}]
Mean[DirichletDistribution[{Subscript[α, 1], Subscript[α, 2], Subscript[α, 3]}]]
→ {Subscript[α, 1]/(Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3]), Subscript[α, 2]/(Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3])}Variance[DirichletDistribution[{Subscript[α, 1], Subscript[α, 2], Subscript[α, 3]}]]
→ {(Subscript[α, 1]*(Subscript[α, 2] + Subscript[α, 3]))/((Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3])^2*(1 + Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3])), (Subscript[α, 2]*(Subscript[α, 1] + Subscript[α, 3]))/((Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3])^2*(1 + Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3]))}PDF[DirichletDistribution[{Subscript[α, 1], Subscript[α, 2], Subscript[α, 3]}], {x, y}]
→ Piecewise[{{(x^(-1 + Subscript[α, 1])*(1 - x - y)^(-1 + Subscript[α, 3])*y^(-1 + Subscript[α, 2])*Gamma[Subscript[α, 1] + Subscript[α, 2] + Subscript[α, 3]])/(Gamma[Subscript[α, 1]]*Gamma[Subscript[α, 2]]*Gamma[Subscript[α, 3]]), x > 0 && y > 0 && 1 - x - y > 0}}, 0] كل الدوال الـ6300 ·
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