ProductDistribution

The joint distribution of $n$ INDEPENDENT $d_1, \ldots, d_n$ — an $n$ -dimensional carrier.

ProductDistribution(d1, ..., dn)the joint distribution of n independent d1, ..., dn.

ProductDistribution({d, n})n independent copies of the same

d

— rewritten to the n-ary form at construction.

Typed signatures

Type	Package	Applies
`((distribution*) -> distribution) & ((list<any>) -> distribution)`	`statistics`	always

Domain: Statistics

Details

$PDF$ at a list $\{x_1,\ldots,x_n\}$ is the product $\prod_i PDF(d_i,x_i)$ ; $CDF$ the product of $CDF(d_i,x_i)$ — both valid only because the factors are assumed independent.
$Mean$ and $Variance$ are componentwise lists, $\{Mean(d_1),\ldots\}$ and $\{Variance(d_1),\ldots\}$ .
RandomVariate draws a list, one independent draw per factor.