This module implements pseudo-random number generators for various distributions.

For integers, uniform selection from a range. For sequences, uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.

On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.

Almost all module functions depend on the basic function `random()`,
which generates a random float uniformly in the semi-open range [0.0,
1.0). Python uses the Mersenne Twister as the core generator. It
produces 53-bit precision floats and has a period of 2**19937-1. The
underlying implementation in C is both fast and threadsafe. The
Mersenne Twister is one of the most extensively tested random number
generators in existence. However, being completely deterministic, it
is not suitable for all purposes, and is completely unsuitable for
cryptographic purposes.

The functions supplied by this module are actually bound methods of a
hidden instance of the `random.Random` class. You can instantiate
your own instances of `Random` to get generators that don’t share
state. This is especially useful for multi-threaded programs,
creating a different instance of `Random` for each thread, and using
the `jumpahead()` method to make it likely that the generated
sequences seen by each thread don’t overlap.

Class `Random` can also be subclassed if you want to use a different
basic generator of your own devising: in that case, override the
`random()`, `seed()`, `getstate()`, `setstate()` and
`jumpahead()` methods. Optionally, a new generator can supply a
`getrandbits()` method — this allows `randrange()` to produce
selections over an arbitrarily large range.

New in version 2.4: the `getrandbits()` method.

As an example of subclassing, the `random` module provides the
`WichmannHill` class that implements an alternative generator in
pure Python. The class provides a backward compatible way to
reproduce results from earlier versions of Python, which used the
Wichmann-Hill algorithm as the core generator. Note that this
Wichmann-Hill generator can no longer be recommended: its period is
too short by contemporary standards, and the sequence generated is
known to fail some stringent randomness tests. See the references
below for a recent variant that repairs these flaws.

Changed in version 2.3: Substituted MersenneTwister for Wichmann-Hill.

Bookkeeping functions:

random.seed([x])

Initialize the basic random number generator. Optional argument

xcan be anyhashableobject. Ifxis omitted orNone, current system time is used; current system time is also used to initialize the generator when the module is first imported. If randomness sources are provided by the operating system, they are used instead of the system time (see theos.urandom()function for details on availability).Changed in version 2.4: formerly, operating system resources were not used.

If

xis notNoneor an int or long,hash(x)is used instead. Ifxis an int or long,xis used directly.

random.getstate()

Return an object capturing the current internal state of the generator. This object can be passed to

setstate()to restore the state.New in version 2.1.

Changed in version 2.6: State values produced in Python 2.6 cannot be loaded into earlier versions.

random.setstate(state)

stateshould have been obtained from a previous call togetstate(), andsetstate()restores the internal state of the generator to what it was at the timesetstate()was called.New in version 2.1.

random.jumpahead(n)

Change the internal state to one different from and likely far away from the current state.

nis a non-negative integer which is used to scramble the current state vector. This is most useful in multi-threaded programs, in conjunction with multiple instances of theRandomclass:setstate()orseed()can be used to force all instances into the same internal state, and thenjumpahead()can be used to force the instances’ states far apart.New in version 2.1.

Changed in version 2.3: Instead of jumping to a specific state,

nsteps ahead,jumpahead(n)jumps to another state likely to be separated by many steps.

random.getrandbits(k)

Returns a python

longint withkrandom bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available,getrandbits()enablesrandrange()to handle arbitrarily large ranges.New in version 2.4.

Functions for integers:

random.randrange([start], stop[, step])

Return a randomly selected element from

range(start, stop, step). This is equivalent tochoice(range(start, stop, step)), but doesn’t actually build a range object.New in version 1.5.2.

random.randint(a, b)

Return a random integerNsuch thata <= N <= b.

Functions for sequences:

random.choice(seq)

Return a random element from the non-empty sequenceseq. Ifseqis empty, raisesIndexError.

random.shuffle(x[, random])

Shuffle the sequence

xin place. The optional argumentrandomis a 0-argument function returning a random float in [0.0, 1.0); by default, this is the functionrandom().Note that for even rather small

len(x), the total number of permutations ofxis larger than the period of most random number generators; this implies that most permutations of a long sequence can never be generated.

random.sample(population, k)

Return a

klength list of unique elements chosen from the population sequence. Used for random sampling without replacement.New in version 2.3.

Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).

Members of the population need not be

hashableor unique. If the population contains repeats, then each occurrence is a possible selection in the sample.To choose a sample from a range of integers, use an

xrange()object as an argument. This is especially fast and space efficient for sampling from a large population:sample(xrange(10000000), 60).

The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.

random.random()

Return the next random floating point number in the range [0.0, 1.0).

random.uniform(a, b)

Return a random floating point number

Nsuch thata <= N <= bfora <= bandb <= N <= aforb < a.The end-point value

bmay or may not be included in the range depending on floating-point rounding in the equationa + (b-a) * random().

random.triangular(low, high, mode)

Return a random floating point number

Nsuch thatlow <= N <= highand with the specifiedmodebetween those bounds. Thelowandhighbounds default to zero and one. Themodeargument defaults to the midpoint between the bounds, giving a symmetric distribution.New in version 2.6.

random.betavariate(alpha, beta)

Beta distribution. Conditions on the parameters arealpha > 0andbeta > 0. Returned values range between 0 and 1.

random.expovariate(lambd)

Exponential distribution.lambdis 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called “lambda”, but that is a reserved word in Python.) Returned values range from 0 to positive infinity iflambdis positive, and from negative infinity to 0 iflambdis negative.

random.gammavariate(alpha, beta)

Gamma distribution. (Notthe gamma function!) Conditions on the parameters arealpha > 0andbeta > 0.

random.gauss(mu, sigma)

Gaussian distribution.muis the mean, andsigmais the standard deviation. This is slightly faster than thenormalvariate()function defined below.

random.lognormvariate(mu, sigma)

Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with meanmuand standard deviationsigma.mucan have any value, andsigmamust be greater than zero.

random.normalvariate(mu, sigma)

Normal distribution.muis the mean, andsigmais the standard deviation.

random.vonmisesvariate(mu, kappa)

muis the mean angle, expressed in radians between 0 and 2**pi*, andkappais the concentration parameter, which must be greater than or equal to zero. Ifkappais equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2**pi*.

random.paretovariate(alpha)

Pareto distribution.alphais the shape parameter.

random.weibullvariate(alpha, beta)

Weibull distribution.alphais the scale parameter andbetais the shape parameter.

Alternative Generators:

class class random.WichmannHill([seed])

Class that implements the Wichmann-Hill algorithm as the core generator. Has all of the same methods asRandomplus thewhseed()method described below. Because this class is implemented in pure Python, it is not threadsafe and may require locks between calls. The period of the generator is 6,953,607,871,644 which is small enough to require care that two independent random sequences do not overlap.

random.whseed([x])

This is obsolete, supplied for bit-level compatibility with versions of Python prior to 2.1. Seeseed()for details.whseed()does not guarantee that distinct integer arguments yield distinct internal states, and can yield no more than about 2**24 distinct internal states in all.

class class random.SystemRandom([seed])

Class that uses the

os.urandom()function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state and sequences are not reproducible. Accordingly, theseed()andjumpahead()methods have no effect and are ignored. Thegetstate()andsetstate()methods raiseNotImplementedErrorif called.New in version 2.4.

Examples of basic usage:

>>> random.random() # Random float x, 0.0 <= x < 1.0 0.37444887175646646 >>> random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0 1.1800146073117523 >>> random.randint(1, 10) # Integer from 1 to 10, endpoints included 7 >>> random.randrange(0, 101, 2) # Even integer from 0 to 100 26 >>> random.choice('abcdefghij') # Choose a random element 'c'>>> items = [1, 2, 3, 4, 5, 6, 7] >>> random.shuffle(items) >>> items [7, 3, 2, 5, 6, 4, 1]>>> random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements [4, 1, 5]

See also:

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3-30 1998.

Wichmann, B. A. & Hill, I. D., “Algorithm AS 183: An efficient and portable pseudo-random number generator”, Applied Statistics 31 (1982) 188-190.

Complementary-Multiply-with-Carry recipe for a compatible alternative random number generator with a long period and comparatively simple update operations.