# 5.3 random -- Generate pseudo-random numbers

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.

The random module supports the Random Number Generator interface, described in section 5.3.1. This interface of the module, as well as the distribution-specific functions described below, all use the pseudo-random generator provided by the whrandom module.

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. These are expected to become part of the Random Number Generator interface in a future release.

betavariate (alpha, beta)
Beta distribution. Conditions on the parameters are `alpha > -1` and `beta > -1`. Returned values range between 0 and 1.

cunifvariate (mean, arc)
Circular uniform distribution. mean is the mean angle, and 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 pi. Returned values will range between `mean - arc/2` and `mean + arc/2`.

expovariate (lambd)
Exponential distribution. 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.

gamma (alpha, beta)
Gamma distribution. (Not the gamma function!) Conditions on the parameters are `alpha > -1` and `beta > 0`.

gauss (mu, sigma)
Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below.

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.

normalvariate (mu, sigma)
Normal distribution. mu is the mean, and sigma is the standard deviation.

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.

paretovariate (alpha)
Pareto distribution. alpha is the shape parameter.

weibullvariate (alpha, beta)
Weibull distribution. alpha is the scale parameter and beta is the shape parameter.