[−][src]Module rand::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
, 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 halfopen 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.
Nonuniform 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 nonuniform distributions; instead
it is recommended that you use either rand_distr
or statrs
.
Reexports
pub use self::weighted::WeightedIndex; 
pub use self::weighted::WeightedError; 
Modules
uniform  A distribution uniformly sampling numbers within a given range. 
weighted  Weighted index sampling 
Structs
Alphanumeric  Sample a 
Bernoulli  The Bernoulli distribution. 
Beta  Deprecated The Beta distribution with shape parameters 
Binomial  Deprecated The binomial distribution 
Cauchy  Deprecated The Cauchy distribution 
ChiSquared  Deprecated The chisquared distribution 
Dirichlet  Deprecated The dirichelet distribution 
DistIter  An iterator that generates random values of 
Exp  Deprecated The exponential distribution 
Exp1  Deprecated Samples floatingpoint numbers according to the exponential distribution,
with rate parameter 
FisherF  Deprecated The Fisher F distribution 
Gamma  Deprecated The Gamma distribution 
LogNormal  Deprecated The lognormal distribution 
Normal  Deprecated The normal distribution 
Open01  A distribution to sample floating point numbers uniformly in the open
interval 
OpenClosed01  A distribution to sample floating point numbers uniformly in the halfopen
interval 
Pareto  Deprecated Samples floatingpoint numbers according to the Pareto distribution 
Poisson  Deprecated The Poisson distribution 
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. 
StandardNormal  Deprecated Samples floatingpoint numbers according to the normal distribution

StudentT  Deprecated The Student t distribution, 
Triangular  Deprecated The triangular distribution. 
Uniform  Sample values uniformly between two bounds. 
UnitCircle  Deprecated Samples uniformly from the edge of the unit circle in two dimensions. 
UnitSphereSurface  Deprecated Samples uniformly from the surface of the unit sphere in three dimensions. 
Weibull  Deprecated Samples floatingpoint numbers according to the Weibull distribution 
Enums
BernoulliError  Error type returned from 
Traits
Distribution  Types (distributions) that can be used to create a random instance of 