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 `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

and`alpha`> -1

. Returned values range between 0 and 1.`beta`> -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

and`mean`-`arc`/2

.`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

and`alpha`> -1

.`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.

**See Also:**

- Module
`whrandom`: - The standard Python random number generator.

See