Random distributions
For maximum flexibility when producing random values, we define the
Distribution
trait:
# #![allow(unused_variables)] #fn main() { // a producer of data of type T: pub trait Distribution<T> { // the key function: fn sample<R: Rng + ?Sized>(&self, rng: &mut R) > T; // a convenience function defined using sample: fn sample_iter<R>(self, rng: R) > DistIter<Self, R, T> where Self: Sized, R: Rng, { ... } } #}
Rand provides implementations of many different distributions; we cover the most
common of these here, but for full details refer to the distributions
module
and the rand_distr
crate.
Uniform distributions
The most obvious type of distribution is the one we already discussed: one without pattern, where each value or range of values is equally likely. This is known as uniform.
Rand actually has several variants of this, repesenting different ranges:
Standard
requires no parameters and samples values uniformly according to the type.Rng::gen
provides a shortcut to this distribution.Uniform
is parametrised byUniform::new(low, high)
(includinglow
, excludinghigh
) orUniform::new_inclusive(low, high)
(including both), and samples values uniformly within this range.Rng::gen_range
is a convenience method defined overUniform::sample_single
, optimised for singlesample usage.Alphanumeric
is uniform over thechar
values09AZaz
.Open01
andOpenClosed01
are provide alternate sampling ranges for floatingpoint types (see below).
Uniform sampling by type
Lets go over the distributions by type:

For
bool
,Standard
samples each value with probability 50%. 
For
Option<T>
, theStandard
distribution samplesNone
with probability 50%, otherwiseSome(value)
is sampled, according to its type. 
For integers (
u8
through tou128
,usize
, andi*
variants),Standard
samples from all possible values whileUniform
samples from the parameterised range. 
For
NonZeroU8
and other "nonzero" types,Standard
samples uniformly from all nonzero values (rejection method). 
Wrapping<T>
integer types are sampled as for the corresponding integer type by theStandard
distribution. 
For floats (
f32
,f64
),Standard
samples from the halfopen range[0, 1)
with 24 or 53 bits of precision (forf32
andf64
respectively)OpenClosed01
samples from the halfopen range(0, 1]
with 24 or 53 bits of precisionOpen01
samples from the open range(0, 1)
with 23 or 52 bits of precisionUniform
samples from a given range with 23 or 52 bits of precision

For the
char
type, theStandard
distribution samples from all available Unicode code points, uniformly; many of these values may not be printable (depending on font support). TheAlphanumeric
samples from only az, AZ and 09 uniformly. 
For tuples and arrays, each element is sampled as above, where supported. The
Standard
andUniform
distributions each support a selection of these types (up to 12tuples and 32element arrays). This includes the empty tuple()
and array. 
For SIMD types, each element is sampled as above, for
Standard
andUniform
(for the latter,low
andhigh
parameters are also SIMD types, effectively sampling from multiple ranges simultaneously). SIMD support is gated behind a feature flag.
Nonuniform distributions
Nonuniform distributions can be divided into two categories, as follows.
Some of these discrete and all of the continuous distributions have been moved
from the main rand
crate to a dedicated rand_distr
crate.
Discrete nonuniform distributions
Discrete distributions sample from boolean or integer types. As above, these can be sampled uniformly, or, as below, via a nonuniform distribution.
Potentially a discrete distribution could sample directly from a set of discrete
values such as a slice or an enum
. See the section on Sequences regarding
Rand's traits for slice and iterator types. Rand does not provide direct
sampling from enum
s, with the exception of Option
(see above).
Booleans
The Bernoulli
distribution is a fancy name for generating a boolean
with a given a probability p
of being true
, or defined via a
success : failure
ratio. Often this is described as a trial with
probability p
of success (true
).
The methods Rng::gen_bool
and Rng::gen_ratio
are shortcuts to this
distribution.
Integers
The Binomial
distribution is related to the Bernoulli
in that it
models running n
independent trials each with probability p
of success,
then counts the number of successes.
Note that for large n
the Binomial
distribution's implementation is
much faster than sampling n
trials individually.
The Poisson
distribution expresses the expected number of events
occurring within a fixed interval, given that events occur with fixed rate λ.
Weighted sequences
The WeightedIndex
distribution samples an index from sequence of weights.
See the Sequences section for convenience wrappers directly sampling a slice
element.
For example, weighted sampling could be used to model the colour of a marble sampled from a bucket containing 5 green, 15 red and 80 blue marbles.
Currently the Rand lib only implements sampling with replacement, i.e. repeated sampling assumes the same distribution (that any sampled marble has been replaced). An alternative distribution implementing sampling without replacement has been requested.
Note also that two implementations of WeightedIndex
are available; the
first is optimised for a small number of samples while
alias_method::WeightedIndex
is optimised for a large number of samples
(where "large" may mean "> 1000"; benchmarks recommended).
Continuous nonuniform distributions
Continuous distributions model samples drawn from the real number line ℝ, or in
some cases a point from a higher dimension (ℝ², ℝ³, etc.). We provide
implementations for f64
and for f32
output in most cases, although currently
the f32
implementations simply reduce the precision of an f64
sample.
The exponential distribution, Exp
, simulates time until decay, assuming a
fixed rate of decay (i.e. exponential decay).
The Normal
distribution (also known as Gaussian) simulates sampling from
the Normal distribution ("Bell curve") with the given mean and standard
deviation. The LogNormal
is related: for sample X
from the lognormal
distribution, log(X)
is normally distributed; this "skews" the normal
distribution to avoid negative values and to have a long positive tail.
The UnitCircle
and UnitSphereSurface
distributions simulate uniform
sampling from the edge of a circle or surface of a sphere.
The Cauchy
distribution (also known as the Lorentz distribution) is the
distribution of the xintercept of a ray from point (x0, γ)
with uniformly
distributed angle.
The Beta
distribution is a twoparameter probability distribution, whose
output values lie between 0 and 1. The Dirichlet
distribution is a
generalisation to any positive number of parameters.