Module distributions

Generating random samples from probability distributions

This module is the home of the Distribution trait and several of its implementations. It is the workhorse behind some of the convenient functionality of the Rng trait, e.g. Rng::gen and of course Rng::sample.

Abstractly, a probability distribution describes the probability of occurrence of each value in its sample space.

More concretely, an implementation of Distribution<T> for type X is an algorithm for choosing values from the sample space (a subset of T) according to the distribution X represents, using an external source of randomness (an RNG supplied to the sample function).

A type X may implement Distribution<T> for multiple types T. Any type implementing Distribution is stateless (i.e. immutable), but it may have internal parameters set at construction time (for example, Uniform allows specification of its sample space as a range within T).

The Standard distribution

The Standard distribution is important to mention. This is the distribution used by Rng::gen and represents the “default” way to produce a random value for many different types, including most primitive types, tuples, arrays, and a few derived types. See the documentation of Standard for more details.

Implementing Distribution<T> for Standard for user types T makes it possible to generate type T with Rng::gen, and by extension also with the random function.

Random characters

Alphanumeric is a simple distribution to sample random letters and numbers of the char type; in contrast Standard may sample any valid char.

Uniform numeric ranges

The Uniform distribution is more flexible than Standard, but also more specialised: it supports fewer target types, but allows the sample space to be specified as an arbitrary range within its target type T. Both Standard and Uniform are in some sense uniform distributions.

Values may be sampled from this distribution using [Rng::sample(Range)] or by creating a distribution object with Uniform::new, Uniform::new_inclusive or From<Range>. When the range limits are not known at compile time it is typically faster to reuse an existing Uniform object than to call [Rng::sample(Range)].

User types T may also implement Distribution<T> for Uniform, although this is less straightforward than for Standard (see the documentation in the uniform module). Doing so enables generation of values of type T with [Rng::sample(Range)].

Open and half-open ranges

There are surprisingly many ways to uniformly generate random floats. A range between 0 and 1 is standard, but the exact bounds (open vs closed) and accuracy differ. In addition to the Standard distribution Rand offers Open01 and OpenClosed01. See “Floating point implementation” section of Standard documentation for more details.

Non-uniform sampling

Sampling a simple true/false outcome with a given probability has a name: the Bernoulli distribution (this is used by Rng::gen_bool).

For weighted sampling from a sequence of discrete values, use the [WeightedIndex] distribution.

This crate no longer includes other non-uniform distributions; instead it is recommended that you use either rand_distr or statrs.

Modules

• uniform
  A distribution uniformly sampling numbers within a given range.

Structs

• Alphanumeric
  Sample a u8, uniformly distributed over ASCII letters and numbers: a-z, A-Z and 0-9.
• Bernoulli
  The Bernoulli distribution.
• DistIter
  An iterator that generates random values of T with distribution D, using R as the source of randomness.
• DistMap
  A distribution of values of type S derived from the distribution D by mapping its output of type T through the closure F.
• Open01
  A distribution to sample floating point numbers uniformly in the open interval (0, 1), i.e. not including either endpoint.
• OpenClosed01
  A distribution to sample floating point numbers uniformly in the half-open interval (0, 1], i.e. including 1 but not 0.
• Slice
  A distribution to sample items uniformly from a slice.
• Standard
  A generic random value distribution, implemented for many primitive types. Usually generates values with a numerically uniform distribution, and with a range appropriate to the type.
• Uniform
  Sample values uniformly between two bounds.

Enums

• BernoulliError
  Error type returned from Bernoulli::new.

Traits

• Distribution
  Types (distributions) that can be used to create a random instance of T.