Bookkeeping functions¶

random.seed(a=None,version=2)¶

Initialize the random number generator.

Ifa is omitted orNone, the current system time is used. Ifrandomness sources are provided by the operating system, they are usedinstead of the system time (see theos.urandom() function for detailson availability).

Ifa is an int, it is used directly.

With version 2 (the default), astr,bytes, orbytearrayobject gets converted to anint and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versionsof Python), the algorithm forstr andbytes generates anarrower range of seeds.

Changed in version 3.2:Moved to the version 2 scheme which uses all of the bits in a string seed.

Deprecated since version 3.9:In the future, theseed must be one of the following types:NoneType,int,float,str,bytes, orbytearray.

random.getstate()¶

Return an object capturing the current internal state of the generator. Thisobject can be passed tosetstate() to restore the state.

random.setstate(state)¶

state should have been obtained from a previous call togetstate(), andsetstate() restores the internal state of the generator to what it was atthe timegetstate() was called.

Functions for bytes¶

random.randbytes(n)¶

Generaten random bytes.

This method should not be used for generating security tokens.Usesecrets.token_bytes() instead.

New in version 3.9.

Functions for integers¶

random.randrange(stop)¶

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

Return a randomly selected element fromrange(start,stop,step). This isequivalent tochoice(range(start,stop,step)), but doesn’t actually build arange object.

The positional argument pattern matches that ofrange(). Keyword argumentsshould not be used because the function may use them in unexpected ways.

Changed in version 3.2:randrange() is more sophisticated about producing equally distributedvalues. Formerly it used a style likeint(random()*n) which could produceslightly uneven distributions.

random.randint(a,b)¶

Return a random integerN such thata<=N<=b. Alias forrandrange(a,b+1).

random.getrandbits(k)¶

Returns a non-negative Python integer withk random bits. This methodis supplied with the MersenneTwister generator and some other generatorsmay also provide it as an optional part of the API. When available,getrandbits() enablesrandrange() to handle arbitrarily largeranges.

Changed in version 3.9:This method now accepts zero fork.

Functions for sequences¶

random.choice(seq)¶

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

random.choices(population,weights=None,*,cum_weights=None,k=1)¶

Return ak sized list of elements chosen from thepopulation with replacement.If thepopulation is empty, raisesIndexError.

If aweights sequence is specified, selections are made according to therelative weights. Alternatively, if acum_weights sequence is given, theselections are made according to the cumulative weights (perhaps computedusingitertools.accumulate()). For example, the relative weights[10,5,30,5] are equivalent to the cumulative weights[10,15,45,50]. Internally, the relative weights are converted tocumulative weights before making selections, so supplying the cumulativeweights saves work.

If neitherweights norcum_weights are specified, selections are madewith equal probability. If a weights sequence is supplied, it must bethe same length as thepopulation sequence. It is aTypeErrorto specify bothweights andcum_weights.

Theweights orcum_weights can use any numeric type that interoperateswith thefloat values returned byrandom() (that includesintegers, floats, and fractions but excludes decimals). Behavior isundefined if any weight is negative. AValueError is raised if allweights are zero.

For a given seed, thechoices() function with equal weightingtypically produces a different sequence than repeated calls tochoice(). The algorithm used bychoices() uses floatingpoint arithmetic for internal consistency and speed. The algorithm usedbychoice() defaults to integer arithmetic with repeated selectionsto avoid small biases from round-off error.

New in version 3.6.

Changed in version 3.9:Raises aValueError if all weights are zero.

random.shuffle(x[,random])¶

Shuffle the sequencex in place.

The optional argumentrandom is a 0-argument function returning a randomfloat in [0.0, 1.0); by default, this is the functionrandom().

To shuffle an immutable sequence and return a new shuffled list, usesample(x,k=len(x)) instead.

Note that even for smalllen(x), the total number of permutations ofxcan quickly grow larger than the period of most random number generators.This implies that most permutations of a long sequence can never begenerated. For example, a sequence of length 2080 is the largest thatcan fit within the period of the Mersenne Twister random number generator.

Deprecated since version 3.9, will be removed in version 3.11:The optional parameterrandom.

random.sample(population,k,*,counts=None)¶

Return ak length list of unique elements chosen from the population sequenceor set. Used for random sampling without replacement.

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

Members of the population need not behashable or unique. If the populationcontains repeats, then each occurrence is a possible selection in the sample.

Repeated elements can be specified one at a time or with the optionalkeyword-onlycounts parameter. For example,sample(['red','blue'],counts=[4,2],k=5) is equivalent tosample(['red','red','red','red','blue','blue'],k=5).

To choose a sample from a range of integers, use arange() object as anargument. This is especially fast and space efficient for sampling from a largepopulation:sample(range(10000000),k=60).

If the sample size is larger than the population size, aValueErroris raised.

Changed in version 3.9:Added thecounts parameter.

Deprecated since version 3.9:In the future, thepopulation must be a sequence. Instances ofset are no longer supported. The set must first be convertedto alist ortuple, preferably in a deterministicorder so that the sample is reproducible.

Real-valued distributions¶

The following functions generate specific real-valued distributions. Functionparameters are named after the corresponding variables in the distribution’sequation, as used in common mathematical practice; most of these equations canbe 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 numberN such thata<=N<=b fora<=b andb<=N<=a forb<a.

The end-point valueb may or may not be included in the rangedepending on floating-point rounding in the equationa+(b-a)*random().

random.triangular(low,high,mode)¶

Return a random floating point numberN such thatlow<=N<=high andwith the specifiedmode between those bounds. Thelow andhigh boundsdefault to zero and one. Themode argument defaults to the midpointbetween the bounds, giving a symmetric distribution.

random.betavariate(alpha,beta)¶

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

random.expovariate(lambd)¶

Exponential distribution.lambd is 1.0 divided by the desiredmean. It should be nonzero. (The parameter would be called“lambda”, but that is a reserved word in Python.) Returned valuesrange from 0 to positive infinity iflambd is positive, and fromnegative infinity to 0 iflambd is negative.

random.gammavariate(alpha,beta)¶

Gamma distribution. (Not the gamma function!) Conditions on theparameters arealpha>0 andbeta>0.

The probability distribution function is:

x**(alpha-1)*math.exp(-x/beta)pdf(x)=--------------------------------------math.gamma(alpha)*beta**alpha

random.gauss(mu,sigma)¶

Gaussian distribution.mu is the mean, andsigma is the standarddeviation. This is slightly faster than thenormalvariate() functiondefined below.

Multithreading note: When two threads call this functionsimultaneously, it is possible that they will receive thesame return value. This can be avoided in three ways.1) Have each thread use a different instance of the randomnumber generator. 2) Put locks around all calls. 3) Use theslower, but thread-safenormalvariate() function instead.

random.lognormvariate(mu,sigma)¶

Log normal distribution. If you take the natural logarithm of thisdistribution, you’ll get a normal distribution with meanmu and standarddeviationsigma.mu can have any value, andsigma must be greater thanzero.

random.normalvariate(mu,sigma)¶

Normal distribution.mu is the mean, andsigma is the standard deviation.

random.vonmisesvariate(mu,kappa)¶

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

random.paretovariate(alpha)¶

Pareto distribution.alpha is the shape parameter.

random.weibullvariate(alpha,beta)¶

Weibull distribution.alpha is the scale parameter andbeta is the shapeparameter.

Alternative Generator¶

classrandom.Random([seed])¶

Class that implements the default pseudo-random number generator used by therandom module.

Deprecated since version 3.9:In the future, theseed must be one of the following types:NoneType,int,float,str,bytes, orbytearray.

classrandom.SystemRandom([seed])¶

Class that uses theos.urandom() function for generating random numbersfrom sources provided by the operating system. Not available on all systems.Does not rely on software state, and sequences are not reproducible. Accordingly,theseed() method has no effect and is ignored.Thegetstate() andsetstate() methods raiseNotImplementedError if called.

Notes on Reproducibility¶

Sometimes it is useful to be able to reproduce the sequences given by apseudo-random number generator. By re-using a seed value, the same sequence should bereproducible from run to run as long as multiple threads are not running.

Most of the random module’s algorithms and seeding functions are subject tochange across Python versions, but two aspects are guaranteed not to change:

• If a new seeding method is added, then a backward compatible seeder will beoffered.

• The generator’srandom() method will continue to produce the samesequence when the compatible seeder is given the same seed.

Examples¶

Basic examples:

>>>random()# Random float:  0.0 <= x < 1.00.37444887175646646>>>uniform(2.5,10.0)# Random float:  2.5 <= x <= 10.03.1800146073117523>>>expovariate(1/5)# Interval between arrivals averaging 5 seconds5.148957571865031>>>randrange(10)# Integer from 0 to 9 inclusive7>>>randrange(0,101,2)# Even integer from 0 to 100 inclusive26>>>choice(['win','lose','draw'])# Single random element from a sequence'draw'>>>deck='ace two three four'.split()>>>shuffle(deck)# Shuffle a list>>>deck['four', 'two', 'ace', 'three']>>>sample([10,20,30,40,50],k=4)# Four samples without replacement[40, 10, 50, 30]

Simulations:

>>># Six roulette wheel spins (weighted sampling with replacement)>>>choices(['red','black','green'],[18,18,2],k=6)['red', 'green', 'black', 'black', 'red', 'black']>>># Deal 20 cards without replacement from a deck>>># of 52 playing cards, and determine the proportion of cards>>># with a ten-value:  ten, jack, queen, or king.>>>dealt=sample(['tens','low cards'],counts=[16,36],k=20)>>>dealt.count('tens')/200.15>>># Estimate the probability of getting 5 or more heads from 7 spins>>># of a biased coin that settles on heads 60% of the time.>>>deftrial():...returnchoices('HT',cum_weights=(0.60,1.00),k=7).count('H')>=5...>>>sum(trial()foriinrange(10_000))/10_0000.4169>>># Probability of the median of 5 samples being in middle two quartiles>>>deftrial():...return2_500<=sorted(choices(range(10_000),k=5))[2]<7_500...>>>sum(trial()foriinrange(10_000))/10_0000.7958

Example ofstatistical bootstrapping using resamplingwith replacement to estimate a confidence interval for the mean of a sample:

# http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htmfromstatisticsimportfmeanasmeanfromrandomimportchoicesdata=[41,50,29,37,81,30,73,63,20,35,68,22,60,31,95]means=sorted(mean(choices(data,k=len(data)))foriinrange(100))print(f'The sample mean of{mean(data):.1f} has a 90% confidence 'f'interval from{means[5]:.1f} to{means[94]:.1f}')

Example of aresampling permutation testto determine the statistical significance orp-value of an observed differencebetween the effects of a drug versus a placebo:

# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilsonfromstatisticsimportfmeanasmeanfromrandomimportshuffledrug=[54,73,53,70,73,68,52,65,65]placebo=[54,51,58,44,55,52,42,47,58,46]observed_diff=mean(drug)-mean(placebo)n=10_000count=0combined=drug+placeboforiinrange(n):shuffle(combined)new_diff=mean(combined[:len(drug)])-mean(combined[len(drug):])count+=(new_diff>=observed_diff)print(f'{n} label reshufflings produced only{count} instances with a difference')print(f'at least as extreme as the observed difference of{observed_diff:.1f}.')print(f'The one-sided p-value of{count/n:.4f} leads us to reject the null')print(f'hypothesis that there is no difference between the drug and the placebo.')

Simulation of arrival times and service deliveries for a multiserver queue:

fromheapqimportheapify,heapreplacefromrandomimportexpovariate,gaussfromstatisticsimportmean,median,stdevaverage_arrival_interval=5.6average_service_time=15.0stdev_service_time=3.5num_servers=3waits=[]arrival_time=0.0servers=[0.0]*num_servers# time when each server becomes availableheapify(servers)foriinrange(1_000_000):arrival_time+=expovariate(1.0/average_arrival_interval)next_server_available=servers[0]wait=max(0.0,next_server_available-arrival_time)waits.append(wait)service_duration=max(0.0,gauss(average_service_time,stdev_service_time))service_completed=arrival_time+wait+service_durationheapreplace(servers,service_completed)print(f'Mean wait:{mean(waits):.1f}.  Stdev wait:{stdev(waits):.1f}.')print(f'Median wait:{median(waits):.1f}.  Max wait:{max(waits):.1f}.')

Recipes¶

The defaultrandom() returns multiples of 2⁻⁵³ in the range0.0 ≤ x < 1.0. All such numbers are evenly spaced and are exactlyrepresentable as Python floats. However, many other representablefloats in that interval are not possible selections. For example,0.05954861408025609 isn’t an integer multiple of 2⁻⁵³.

The following recipe takes a different approach. All floats in theinterval are possible selections. The mantissa comes from a uniformdistribution of integers in the range2⁵² ≤ mantissa < 2⁵³. Theexponent comes from a geometric distribution where exponents smallerthan-53 occur half as often as the next larger exponent.

fromrandomimportRandomfrommathimportldexpclassFullRandom(Random):defrandom(self):mantissa=0x10_0000_0000_0000|self.getrandbits(52)exponent=-53x=0whilenotx:x=self.getrandbits(32)exponent+=x.bit_length()-32returnldexp(mantissa,exponent)

Allreal valued distributionsin the class will use the new method:

>>>fr=FullRandom()>>>fr.random()0.05954861408025609>>>fr.expovariate(0.25)8.87925541791544

The recipe is conceptually equivalent to an algorithm that chooses fromall the multiples of 2⁻¹⁰⁷⁴ in the range0.0 ≤ x < 1.0. All suchnumbers are evenly spaced, but most have to be rounded down to thenearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallestpositive unnormalized float and is equal tomath.ulp(0.0).)