MarginalDistribution

The $k$-th marginal factor of a ProductDistribution — or the joint marginal of several.

MarginalDistribution(ProductDistribution(d1, ..., dn), k)the k-th factor, dk, directly.

MarginalDistribution(ProductDistribution(d1, ..., dn), {k1, k2, ...})ProductDistribution(dk1, dk2, ...), the joint marginal of the named factors.

Typed signatures

Type	Package	Applies
(expression<ProductDistribution>, integer | list<integer>) -> distribution	statistics	always

Domain: Statistics

Details

• Reduces away entirely at evaluation — the result IS the plain factor (or a ProductDistribution of the selected factors), so PDF/CDF/Mean/Variance/RandomVariate on it are just whatever that reduced distribution already answers.
• Only defined over a ProductDistribution base (independence is what makes "the k-th marginal" simply "the k-th factor") — any other first argument stays unevaluated.

Examples

Basic #

live ↗

In$\mathrm{MarginalDistribution}(\mathrm{ProductDistribution}(\operatorname{NormalDistribution}(0, 1), \operatorname{NormalDistribution}(5, 2)), 2)$Out$\operatorname{NormalDistribution}(5, 2)$

live ↗

In$\mathrm{mean}(\mathrm{MarginalDistribution}(\mathrm{ProductDistribution}(\operatorname{NormalDistribution}(0, 1), \operatorname{NormalDistribution}(5, 2)), 2))$Out$5$

live ↗

In$\mathrm{MarginalDistribution}(\mathrm{ProductDistribution}(\operatorname{NormalDistribution}(0, 1), \operatorname{NormalDistribution}(5, 2), \operatorname{NormalDistribution}(9, 1)), \bigl\lbrack1, 3\bigr\rbrack)$Out$\mathrm{ProductDistribution}(\operatorname{NormalDistribution}(0, 1), \operatorname{NormalDistribution}(9, 1))$

About

Examples	3

See also: ProductDistribution, Mean