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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, Rng::gen_range and of course Rng::sample.

Abstractly, a probability distribution describes the probability of occurance 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::gen_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 distribution object than to call Rng::gen_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::gen_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 weighted module.

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

Re-exports

pub use self::weighted::WeightedError;
pub use self::weighted::WeightedIndex;

Modules

bernoulli 🔒

The Bernoulli distribution.

binomial 🔒

The binomial distribution.

cauchy 🔒

The Cauchy distribution.

dirichlet 🔒

The dirichlet distribution.

The exponential distribution.

float 🔒

Basic floating-point number distributions

gamma 🔒

The Gamma and derived distributions.

integer 🔒

The implementations of the Standard distribution for integer types.

normal 🔒

The normal and derived distributions.

other 🔒

The implementations of the Standard distribution for other built-in types.

pareto 🔒

The Pareto distribution.

poisson 🔒

The Poisson distribution.

triangular 🔒

The triangular distribution.

A distribution uniformly sampling numbers within a given range.

utils 🔒

Math helper functions

weibull 🔒

The Weibull distribution.

Weighted index sampling

Structs

Sample a char, uniformly distributed over ASCII letters and numbers: a-z, A-Z and 0-9.

The Bernoulli distribution.

BetaDeprecated

The Beta distribution with shape parameters alpha and beta.

BinomialDeprecated

The binomial distribution Binomial(n, p).

CauchyDeprecated

The Cauchy distribution Cauchy(median, scale).

ChiSquaredDeprecated

The chi-squared distribution χ²(k), where k is the degrees of freedom.

DirichletDeprecated

The dirichelet distribution Dirichlet(alpha).

An iterator that generates random values of T with distribution D, using R as the source of randomness.

ExpDeprecated

The exponential distribution Exp(lambda).

Exp1Deprecated

Samples floating-point numbers according to the exponential distribution, with rate parameter λ = 1. This is equivalent to Exp::new(1.0) or sampling with -rng.gen::<f64>().ln(), but faster.

FisherFDeprecated

The Fisher F distribution F(m, n).

GammaDeprecated

The Gamma distribution Gamma(shape, scale) distribution.

LogNormalDeprecated

The log-normal distribution ln N(mean, std_dev**2).

NormalDeprecated

The normal distribution N(mean, std_dev**2).

A distribution to sample floating point numbers uniformly in the open interval (0, 1), i.e. not including either endpoint.

A distribution to sample floating point numbers uniformly in the half-open interval (0, 1], i.e. including 1 but not 0.

ParetoDeprecated

Samples floating-point numbers according to the Pareto distribution

PoissonDeprecated

The Poisson distribution Poisson(lambda).

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.

StandardNormalDeprecated

Samples floating-point numbers according to the normal distribution N(0, 1) (a.k.a. a standard normal, or Gaussian). This is equivalent to Normal::new(0.0, 1.0) but faster.

StudentTDeprecated

The Student t distribution, t(nu), where nu is the degrees of freedom.

TriangularDeprecated

The triangular distribution.

Sample values uniformly between two bounds.

UnitCircleDeprecated

Samples uniformly from the edge of the unit circle in two dimensions.

Samples uniformly from the surface of the unit sphere in three dimensions.

WeibullDeprecated

Samples floating-point numbers according to the Weibull distribution

Enums

Error type returned from Bernoulli::new.

Traits

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