\section{\module{random} ---
         Generate pseudo-random numbers}

\declaremodule{standard}{random}
\modulesynopsis{Generate pseudo-random numbers with various common
                distributions.}


This module implements pseudo-random number generators for various
distributions: on the real line, there are functions to compute normal
or Gaussian, lognormal, negative exponential, gamma, and beta
distributions.  For generating distribution of angles, the circular
uniform and von Mises distributions are available.


\begin{funcdesc}{choice}{seq}
  Chooses a random element from the non-empty sequence \var{seq} and
  returns it.
\end{funcdesc}

\begin{funcdesc}{randint}{a, b}
  \deprecated{2.0}{Use \function{randrange()} instead.}
  Returns a random integer \var{N} such that
  \code{\var{a} <= \var{N} <= \var{b}}.
\end{funcdesc}

\begin{funcdesc}{random}{}
  Returns the next random floating point number in the range [0.0,
  1.0).
\end{funcdesc}

\begin{funcdesc}{randrange}{\optional{start,} stop\optional{, step}}
  Return a randomly selected element from \code{range(\var{start},
  \var{stop}, \var{step})}.  This is equivalent to
  \code{choice(range(\var{start}, \var{stop}, \var{step}))}.
  \versionadded{1.5.2}
\end{funcdesc}

\begin{funcdesc}{uniform}{a, b}
  Returns a random real number \var{N} such that
  \code{\var{a} <= \var{N} < \var{b}}.
\end{funcdesc}


The following functions are defined to support specific distributions,
and all return real values.  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.


\begin{funcdesc}{betavariate}{alpha, beta}
  Beta distribution.  Conditions on the parameters are
  \code{\var{alpha} > -1} and \code{\var{beta} > -1}.
  Returned values range between 0 and 1.
\end{funcdesc}

\begin{funcdesc}{cunifvariate}{mean, arc}
  Circular uniform distribution.  \var{mean} is the mean angle, and
  \var{arc} is the range of the distribution, centered around the mean
  angle.  Both values must be expressed in radians, and can range
  between 0 and \emph{pi}.  Returned values will range between
  \code{\var{mean} - \var{arc}/2} and \code{\var{mean} +
  \var{arc}/2}.
\end{funcdesc}

\begin{funcdesc}{expovariate}{lambd}
  Exponential distribution.  \var{lambd} is 1.0 divided by the desired
  mean.  (The parameter would be called ``lambda'', but that is a
  reserved word in Python.)  Returned values will range from 0 to
  positive infinity.
\end{funcdesc}

\begin{funcdesc}{gamma}{alpha, beta}
  Gamma distribution.  (\emph{Not} the gamma function!)  Conditions on
  the parameters are \code{\var{alpha} > -1} and \code{\var{beta} > 0}.
\end{funcdesc}

\begin{funcdesc}{gauss}{mu, sigma}
  Gaussian distribution.  \var{mu} is the mean, and \var{sigma} is the
  standard deviation.  This is slightly faster than the
  \function{normalvariate()} function defined below.
\end{funcdesc}

\begin{funcdesc}{lognormvariate}{mu, sigma}
  Log normal distribution.  If you take the natural logarithm of this
  distribution, you'll get a normal distribution with mean \var{mu}
  and standard deviation \var{sigma}.  \var{mu} can have any value,
  and \var{sigma} must be greater than zero.  
\end{funcdesc}

\begin{funcdesc}{normalvariate}{mu, sigma}
  Normal distribution.  \var{mu} is the mean, and \var{sigma} is the
  standard deviation.
\end{funcdesc}

\begin{funcdesc}{vonmisesvariate}{mu, kappa}
  \var{mu} is the mean angle, expressed in radians between 0 and
  2*\emph{pi}, and \var{kappa} is the concentration parameter, which
  must be greater than or equal to zero.  If \var{kappa} is equal to
  zero, this distribution reduces to a uniform random angle over the
  range 0 to 2*\emph{pi}.
\end{funcdesc}

\begin{funcdesc}{paretovariate}{alpha}
  Pareto distribution.  \var{alpha} is the shape parameter.
\end{funcdesc}

\begin{funcdesc}{weibullvariate}{alpha, beta}
  Weibull distribution.  \var{alpha} is the scale parameter and
  \var{beta} is the shape parameter.
\end{funcdesc}


This function does not represent a specific distribution, but
implements a standard useful algorithm:

\begin{funcdesc}{shuffle}{x\optional{, random}}
  Shuffle the sequence \var{x} in place.
  The optional argument \var{random} is a 0-argument function
  returning a random float in [0.0, 1.0); by default, this is the
  function \function{random()}.

  Note that for even rather small \code{len(\var{x})}, the total
  number of permutations of \var{x} is larger than the period of most
  random number generators; this implies that most permutations of a
  long sequence can never be generated.
\end{funcdesc}


\begin{seealso}
  \seemodule{whrandom}{The standard Python pseudo-random number
                       generator.}
\end{seealso}