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Title: random — Generate pseudo-random numbers — Python 3.13.18 documentation
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random — Generate pseudo-random numbers — Python 3.13.18 documentation Navigation index modules | next | previous | Python » 3.13.18 Documentation » The Python standard library » Numeric and Mathematical Modules » random — Generate pseudo-random numbers | Theme Auto Light Dark | random — Generate pseudo-random numbers¶ Source code: Lib/random.py This module implements pseudo-random number generators for various distributions. For integers, there is uniform selection from a range. For sequences, there is 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 half-open range 0.0 0 and beta 0. Returned values range between 0 and 1. random.expovariate(lambd=1.0)¶ Exponential distribution. lambd is 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 if lambd is positive, and from negative infinity to 0 if lambd is negative. Changed in version 3.12: Added the default value for lambd. random.gammavariate(alpha, beta)¶ Gamma distribution. (Not the gamma function!) The shape and scale parameters, alpha and beta, must have positive values. (Calling conventions vary and some sources define ‘beta’ as the inverse of the scale). The probability distribution function is: x ** (alpha - 1) * math.exp(-x / beta) pdf(x) = -------------------------------------- math.gamma(alpha) * beta ** alpha random.gauss(mu=0.0, sigma=1.0)¶ Normal distribution, also called the Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below. Multithreading note: When two threads call this function simultaneously, it is possible that they will receive the same return value. This can be avoided in three ways. 1) Have each thread use a different instance of the random number generator. 2) Put locks around all calls. 3) Use the slower, but thread-safe normalvariate() function instead. Changed in version 3.11: mu and sigma now have default arguments. random.lognormvariate(mu, sigma)¶ Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean mu and standard deviation sigma. mu can have any value, and sigma must be greater than zero. random.normalvariate(mu=0.0, sigma=1.0)¶ Normal distribution. mu is the mean, and sigma is the standard deviation. Changed in version 3.11: mu and sigma now have default arguments. random.vonmisesvariate(mu, kappa)¶ mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over 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 and beta is the shape parameter. Alternative Generator¶ class random.Random([seed])¶ Class that implements the default pseudo-random number generator used by the random module. Changed in version 3.11: Formerly the seed could be any hashable object. Now it is limited to: None, int, float, str, bytes, or bytearray. Subclasses of Random should override the following methods if they wish to make use of a different basic generator: seed(a=None, version=2)¶ Override this method in subclasses to customise the seed() behaviour of Random instances. getstate()¶ Override this method in subclasses to customise the getstate() behaviour of Random instances. setstate(state)¶ Override this method in subclasses to customise the setstate() behaviour of Random instances. random()¶ Override this method in subclasses to customise the random() behaviour of Random instances. Optionally, a custom generator subclass can also supply the following method: getrandbits(k)¶ Override this method in subclasses to customise the getrandbits() behaviour of Random instances. randbytes(n)¶ Override this method in subclasses to customise the randbytes() behaviour of Random instances. 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, the seed() method has no effect and is ignored. The getstate() and setstate() methods raise NotImplementedError if called. Notes on Reproducibility¶ Sometimes it is useful to be able to reproduce the sequences given by a pseudo-random number generator. By reusing a seed value, the same sequence should be reproducible from run to run as long as multiple threads are not running. Most of the random module’s algorithms and seeding functions are subject to change across Python versions, but two aspects are guaranteed not to change: If a new seeding method is added, then a backward compatible seeder will be offered. The generator’s random() method will continue to produce the same sequence when the compatible seeder is given the same seed. Examples¶ Basic examples: random() # Random float: 0.0 uniform(2.5, 10.0) # Random float: 2.5 expovariate(1 / 5) # Interval between arrivals averaging 5 seconds 5.148957571865031 randrange(10) # Integer from 0 to 9 inclusive 7 randrange(0, 101, 2) # Even integer from 0 to 100 inclusive 26 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. deal = sample(['tens', 'low cards'], counts=[16, 36], k=20) deal.count('tens') / 20 0.15 # Estimate the probability of getting 5 or more heads from 7 spins # of a biased coin that settles on heads 60% of the time. sum(binomialvariate(n=7, p=0.6) = 5 for i in range(10_000)) / 10_000 0.4169 # Probability of the median of 5 samples being in middle two quartiles def trial(): ... return 2_500 sum(trial() for i in range(10_000)) / 10_000 0.7958 Example of statistical bootstrapping using resampling with replacement to estimate a confidence interval for the mean of a sample: # https://www.thoughtco.com/example-of-bootstrapping-3126155 from statistics import fmean as mean from random import choices data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95] means = sorted(mean(choices(data, k=len(data))) for i in range(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 a resampling permutation test to determine the statistical significance or p-value of an observed difference between the effects of a drug versus a placebo: # Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson from statistics import fmean as mean from random import shuffle drug = [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_000 count = 0 combined = drug + placebo for i in range(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: from heapq import heapify, heapreplace from random import expovariate, gauss from statistics import mean, quantiles average_arrival_interval = 5.6 average_service_time = 15.0 stdev_service_time = 3.5 num_servers = 3 waits = [] arrival_time = 0.0 servers = [0.0] * num_servers # time when each server becomes available heapify(servers) for i in range(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_duration heapreplace(servers, service_completed) print(f'Mean wait: {mean(waits):.1f} Max wait: {max(waits):.1f}') print('Quartiles:', [round(q, 1) for q in quantiles(waits)]) See also Statistics for Hackers a video tutorial by Jake Vanderplas on statistical analysis using just a few fundamental concepts including simulation, sampling, shuffling, and cross-validation. Economics Simulation a simulation of a marketplace by Peter Norvig that shows effective use of many of the tools and distributions provided by this module (gauss, uniform, sample, betavariate, choice, triangular, and randrange). A Concrete Introduction to Probability (using Python) a tutorial by Peter Norvig covering the basics of probability theory, how to write simulations, and how to perform data analysis using Python. Recipes¶ These recipes show how to efficiently make random selections from the combinatoric iterators in the itertools module: import random def random_product(*iterables, repeat=1): "Random selection from itertools.product(*iterables, repeat=repeat)" pools = tuple(map(tuple, iterables)) * repeat return tuple(map(random.choice, pools)) def random_permutation(iterable, r=None): "Random selection from itertools.permutations(iterable, r)" pool = tuple(iterable) r = len(pool) if r is None else r return tuple(random.sample(pool, r)) def random_combination(iterable, r): "Random selection from itertools.combinations(iterable, r)" pool = tuple(iterable) n = len(pool) indices = sorted(random.sample(range(n), r)) return tuple(pool[i] for i in indices) def random_combination_with_replacement(iterable, r): "Choose r elements with replacement. Order the result to match the iterable." # Result will be in set(itertools.combinations_with_replacement(iterable, r)). pool = tuple(iterable) n = len(pool) indices = sorted(random.choices(range(n), k=r)) return tuple(pool[i] for i in indices) def random_derangement(iterable): "Choose a permutation where no element stays in its original position." seq = tuple(iterable) if len(seq) fr = FullRandom() fr.random() 0.05954861408025609 fr.expovariate(0.25) 8.87925541791544 The recipe is conceptually equivalent to an algorithm that chooses from all the multiples of 2⁻¹⁰⁷⁴ in the range 0.0 ≤ x ¶ --integer ¶ Print a random integer between 1 and N inclusive, using randint(). -f ¶ --float ¶ Print a random floating-point number between 0 and N inclusive, using uniform(). If no options are given, the output depends on the input: String or multiple: same as --choice. Integer: same as --integer. Float: same as --float. Command-line example¶ Here are some examples of the random command-line interface: $ # Choose one at random $ python -m random egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce" Lobster Thermidor aux crevettes with a Mornay sauce $ # Random integer $ python -m random 6 6 $ # Random floating-point number $ python -m random 1.8 1.7080016272295635 $ # With explicit arguments $ python -m random --choice egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce" egg $ python -m random --integer 6 3 $ python -m random --float 1.8 1.5666339105010318 $ python -m random --integer 6 5 $ python -m random --float 6 3.1942323316565915 Table of Contents random — Generate pseudo-random numbers Bookkeeping functions Functions for bytes Functions for integers Functions for sequences Discrete distributions Real-valued distributions Alternative Generator Notes on Reproducibility Examples Recipes Command-line usage Command-line example Previous topic fractions — Rational numbers Next topic statistics — Mathematical statistics functions This page Report a bug Show source « Navigation index modules | next | previous | Python » 3.13.18 Documentation » The Python standard library » Numeric and Mathematical Modules » random — Generate pseudo-random numbers | Theme Auto Light Dark | © Copyright 2001-2026, Python Software Foundation. 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