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2f726e9093
* Added C coded getrandbits(k) method that runs in linear time. * Call the new method from randrange() for ranges >= 2**53. * Adds a warning for generators not defining getrandbits() whenever they have a call to randrange() with too large of a population.
260 lines
10 KiB
TeX
260 lines
10 KiB
TeX
\section{\module{random} ---
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Generate pseudo-random numbers}
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\declaremodule{standard}{random}
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\modulesynopsis{Generate pseudo-random numbers with various common
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distributions.}
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This module implements pseudo-random number generators for various
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distributions.
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For integers, uniform selection from a range.
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For sequences, uniform selection of a random element, a function to
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generate a random permutation of a list in-place, and a function for
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random sampling without replacement.
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On the real line, there are functions to compute uniform, normal (Gaussian),
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lognormal, negative exponential, gamma, and beta distributions.
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For generating distributions of angles, the von Mises distribution
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is available.
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Almost all module functions depend on the basic function
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\function{random()}, which generates a random float uniformly in
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the semi-open range [0.0, 1.0). Python uses the Mersenne Twister as
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the core generator. It produces 53-bit precision floats and has a
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period of 2**19937-1. The underlying implementation in C
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is both fast and threadsafe. The Mersenne Twister is one of the most
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extensively tested random number generators in existence. However, being
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completely deterministic, it is not suitable for all purposes, and is
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completely unsuitable for cryptographic purposes.
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The functions supplied by this module are actually bound methods of a
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hidden instance of the \class{random.Random} class. You can
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instantiate your own instances of \class{Random} to get generators
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that don't share state. This is especially useful for multi-threaded
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programs, creating a different instance of \class{Random} for each
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thread, and using the \method{jumpahead()} method to ensure that the
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generated sequences seen by each thread don't overlap.
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Class \class{Random} can also be subclassed if you want to use a
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different basic generator of your own devising: in that case, override
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the \method{random()}, \method{seed()}, \method{getstate()},
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\method{setstate()} and \method{jumpahead()} methods.
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Optionally, a new generator can supply a \method{getrandombits()}
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method --- this allows \method{randrange()} to produce selections
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over an arbitrarily large range.
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\versionadded[the \method{getrandombits()} method]{2.4}
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As an example of subclassing, the \module{random} module provides
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the \class{WichmannHill} class which implements an alternative generator
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in pure Python. The class provides a backward compatible way to
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reproduce results from earlier versions of Python which used the
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Wichmann-Hill algorithm as the core generator.
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\versionchanged[Substituted MersenneTwister for Wichmann-Hill]{2.3}
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Bookkeeping functions:
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\begin{funcdesc}{seed}{\optional{x}}
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Initialize the basic random number generator.
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Optional argument \var{x} can be any hashable object.
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If \var{x} is omitted or \code{None}, current system time is used;
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current system time is also used to initialize the generator when the
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module is first imported.
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If \var{x} is not \code{None} or an int or long,
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\code{hash(\var{x})} is used instead.
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If \var{x} is an int or long, \var{x} is used directly.
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\end{funcdesc}
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\begin{funcdesc}{getstate}{}
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Return an object capturing the current internal state of the
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generator. This object can be passed to \function{setstate()} to
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restore the state.
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\versionadded{2.1}
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\end{funcdesc}
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\begin{funcdesc}{setstate}{state}
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\var{state} should have been obtained from a previous call to
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\function{getstate()}, and \function{setstate()} restores the
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internal state of the generator to what it was at the time
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\function{setstate()} was called.
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\versionadded{2.1}
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\end{funcdesc}
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\begin{funcdesc}{jumpahead}{n}
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Change the internal state to one different from and likely far away from
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the current state. \var{n} is a non-negative integer which is used to
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scramble the current state vector. This is most useful in multi-threaded
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programs, in conjuction with multiple instances of the \class{Random}
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class: \method{setstate()} or \method{seed()} can be used to force all
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instances into the same internal state, and then \method{jumpahead()}
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can be used to force the instances' states far apart.
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\versionadded{2.1}
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\versionchanged[Instead of jumping to a specific state, \var{n} steps
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ahead, \method{jumpahead(\var{n})} jumps to another state likely to be
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separated by many steps.]{2.3}
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\end{funcdesc}
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\begin{funcdesc}{getrandbits}{k}
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Returns a python \class{long} int with \var{k} random bits.
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This method is supplied with the MersenneTwister generator and some
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other generators may also provide it as an optional part of the API.
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When available, \method{getrandbits()} enables \method{randrange()}
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to handle arbitrarily large ranges.
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\versionadded{2.4}
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\end{funcdesc}
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Functions for integers:
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\begin{funcdesc}{randrange}{\optional{start,} stop\optional{, step}}
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Return a randomly selected element from \code{range(\var{start},
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\var{stop}, \var{step})}. This is equivalent to
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\code{choice(range(\var{start}, \var{stop}, \var{step}))},
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but doesn't actually build a range object.
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\versionadded{1.5.2}
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\end{funcdesc}
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\begin{funcdesc}{randint}{a, b}
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Return a random integer \var{N} such that
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\code{\var{a} <= \var{N} <= \var{b}}.
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\end{funcdesc}
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Functions for sequences:
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\begin{funcdesc}{choice}{seq}
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Return a random element from the non-empty sequence \var{seq}.
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\end{funcdesc}
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\begin{funcdesc}{shuffle}{x\optional{, random}}
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Shuffle the sequence \var{x} in place.
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The optional argument \var{random} is a 0-argument function
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returning a random float in [0.0, 1.0); by default, this is the
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function \function{random()}.
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Note that for even rather small \code{len(\var{x})}, the total
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number of permutations of \var{x} is larger than the period of most
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random number generators; this implies that most permutations of a
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long sequence can never be generated.
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\end{funcdesc}
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\begin{funcdesc}{sample}{population, k}
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Return a \var{k} length list of unique elements chosen from the
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population sequence. Used for random sampling without replacement.
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\versionadded{2.3}
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Returns a new list containing elements from the population while
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leaving the original population unchanged. The resulting list is
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in selection order so that all sub-slices will also be valid random
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samples. This allows raffle winners (the sample) to be partitioned
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into grand prize and second place winners (the subslices).
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Members of the population need not be hashable or unique. If the
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population contains repeats, then each occurrence is a possible
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selection in the sample.
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To choose a sample from a range of integers, use \function{xrange}
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as an argument. This is especially fast and space efficient for
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sampling from a large population: \code{sample(xrange(10000000), 60)}.
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\end{funcdesc}
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The following functions generate specific real-valued distributions.
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Function parameters are named after the corresponding variables in the
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distribution's equation, as used in common mathematical practice; most of
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these equations can be found in any statistics text.
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\begin{funcdesc}{random}{}
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Return the next random floating point number in the range [0.0, 1.0).
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\end{funcdesc}
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\begin{funcdesc}{uniform}{a, b}
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Return a random real number \var{N} such that
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\code{\var{a} <= \var{N} < \var{b}}.
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\end{funcdesc}
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\begin{funcdesc}{betavariate}{alpha, beta}
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Beta distribution. Conditions on the parameters are
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\code{\var{alpha} > -1} and \code{\var{beta} > -1}.
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Returned values range between 0 and 1.
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\end{funcdesc}
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\begin{funcdesc}{expovariate}{lambd}
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Exponential distribution. \var{lambd} is 1.0 divided by the desired
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mean. (The parameter would be called ``lambda'', but that is a
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reserved word in Python.) Returned values range from 0 to
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positive infinity.
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\end{funcdesc}
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\begin{funcdesc}{gammavariate}{alpha, beta}
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Gamma distribution. (\emph{Not} the gamma function!) Conditions on
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the parameters are \code{\var{alpha} > 0} and \code{\var{beta} > 0}.
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\end{funcdesc}
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\begin{funcdesc}{gauss}{mu, sigma}
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Gaussian distribution. \var{mu} is the mean, and \var{sigma} is the
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standard deviation. This is slightly faster than the
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\function{normalvariate()} function defined below.
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\end{funcdesc}
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\begin{funcdesc}{lognormvariate}{mu, sigma}
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Log normal distribution. If you take the natural logarithm of this
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distribution, you'll get a normal distribution with mean \var{mu}
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and standard deviation \var{sigma}. \var{mu} can have any value,
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and \var{sigma} must be greater than zero.
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\end{funcdesc}
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\begin{funcdesc}{normalvariate}{mu, sigma}
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Normal distribution. \var{mu} is the mean, and \var{sigma} is the
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standard deviation.
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\end{funcdesc}
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\begin{funcdesc}{vonmisesvariate}{mu, kappa}
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\var{mu} is the mean angle, expressed in radians between 0 and
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2*\emph{pi}, and \var{kappa} is the concentration parameter, which
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must be greater than or equal to zero. If \var{kappa} is equal to
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zero, this distribution reduces to a uniform random angle over the
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range 0 to 2*\emph{pi}.
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\end{funcdesc}
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\begin{funcdesc}{paretovariate}{alpha}
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Pareto distribution. \var{alpha} is the shape parameter.
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\end{funcdesc}
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\begin{funcdesc}{weibullvariate}{alpha, beta}
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Weibull distribution. \var{alpha} is the scale parameter and
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\var{beta} is the shape parameter.
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\end{funcdesc}
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Alternative Generator
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\begin{classdesc}{WichmannHill}{\optional{seed}}
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Class that implements the Wichmann-Hill algorithm as the core generator.
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Has all of the same methods as \class{Random} plus the \method{whseed}
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method described below. Because this class is implemented in pure
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Python, it is not threadsafe and may require locks between calls. The
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period of the generator is 6,953,607,871,644 which is small enough to
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require care that two independent random sequences do not overlap.
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\end{classdesc}
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\begin{funcdesc}{whseed}{\optional{x}}
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This is obsolete, supplied for bit-level compatibility with versions
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of Python prior to 2.1.
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See \function{seed} for details. \function{whseed} does not guarantee
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that distinct integer arguments yield distinct internal states, and can
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yield no more than about 2**24 distinct internal states in all.
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\end{funcdesc}
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\begin{seealso}
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\seetext{M. Matsumoto and T. Nishimura, ``Mersenne Twister: A
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623-dimensionally equidistributed uniform pseudorandom
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number generator'',
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\citetitle{ACM Transactions on Modeling and Computer Simulation}
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Vol. 8, No. 1, January pp.3-30 1998.}
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\seetext{Wichmann, B. A. \& Hill, I. D., ``Algorithm AS 183:
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An efficient and portable pseudo-random number generator'',
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\citetitle{Applied Statistics} 31 (1982) 188-190.}
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\end{seealso}
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