RandomVariate

A random draw from a distribution, or a list of them -- Random over the distribution, by its Wolfram name.

RandomVariate(dist)one draw.

RandomVariate(dist, n)a list of $n$ draws.

Typed signatures

Type	Package	Applies
(any, integer<0..>?) random -> any	statistics	always

Domain: Statistics

Details

• Seeded, not free-running — same convention as SeedRandom/RandomInteger in @enumeratio/combinatorics/collections: call SeedRandom(seed) first for a reproducible sequence; without it, a fixed default seed makes even a bare call reproducible run to run. This file's draws are their OWN stream, independent of RandomInteger's, even after the same SeedRandom call — a follow-up once collections' own seeded RandomInteger lands is to unify both under one engine-level generator.
• The generator is our own (mulberry32, the same algorithm RandomInteger uses), not Wolfram's — the same seed draws a different sequence. Only the shape and (for NormalDistribution/UniformDistribution/…) approximate range of the answer are guaranteed to match.
• Sampling method by distribution — NormalDistribution/BinormalDistribution: Box–Muller; UniformDistribution: inverse CDF; PoissonDistribution: Knuth's algorithm; BinomialDistribution: a sum of Bernoulli draws; GammaDistribution/BetaDistribution: Marsaglia–Tsang; EmpiricalDistribution: uniform resampling with replacement.

Examples

Basic #

With no SeedRandom call, a fixed default seed still makes this reproducible

live ↗

In$\mathrm{RandomVariate}(\operatorname{NormalDistribution}(0, 1))$Out$-0.956\,162\,229\,384\,149$

Scope #

live ↗

In$\mathrm{Last}(\bigl\lbrack\mathrm{SeedRandom}(1), \mathrm{RandomVariate}(\operatorname{UniformDistribution}(\bigl\lbrack0, 1\bigr\rbrack), 3)\bigr\rbrack)$Out$\bigl\lbrack0.627\,073\,940\,588\,161\,3, 0.002\,735\,721\,180\,215\,478, 0.527\,447\,039\,959\,952\,2\bigr\rbrack$

live ↗

In$\mathrm{Last}(\bigl\lbrack\mathrm{SeedRandom}(1), \mathrm{RandomVariate}(\operatorname{PoissonDistribution}(4))\bigr\rbrack)$Out$1$

live ↗

In$\mathrm{Last}(\bigl\lbrack\mathrm{SeedRandom}(2), \mathrm{RandomVariate}(\mathrm{EmpiricalDistribution}(\bigl\lbrack a, b, c\bigr\rbrack))\bigr\rbrack)$Out$c$

Properties & Relations #

RandomVariate is Random over the distribution: the same draw from the same stream

live ↗

In$\mathrm{Last}(\bigl\lbrack\mathrm{SeedRandom}(5), \mathrm{RandomVariate}(\operatorname{NormalDistribution}(0, 1))\bigr\rbrack)=\mathrm{Last}(\bigl\lbrack\mathrm{SeedRandom}(5), \mathrm{Random}(\operatorname{NormalDistribution}(0, 1))\bigr\rbrack)$Out$\mathrm{True}$

About

Examples	5

See also: SeedRandom, Distributed