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# simulation::random(n) 0.4 tcllib "Tcl Simulation Tools"

## Name

simulation::random - Pseudo-random number generators

## Synopsis

- package require Tcl ?8.4?
- package require simulation::random 0.4

- ::simulation::random::prng_Bernoulli p
- ::simulation::random::prng_Discrete n
- ::simulation::random::prng_Poisson lambda
- ::simulation::random::prng_Uniform min max
- ::simulation::random::prng_Triangular min max
- ::simulation::random::prng_SymmTriangular min max
- ::simulation::random::prng_Exponential min mean
- ::simulation::random::prng_Normal mean stdev
- ::simulation::random::prng_Pareto min steep
- ::simulation::random::prng_Gumbel min f
- ::simulation::random::prng_chiSquared df
- ::simulation::random::prng_Disk rad
- ::simulation::random::prng_Sphere rad
- ::simulation::random::prng_Ball rad
- ::simulation::random::prng_Rectangle length width
- ::simulation::random::prng_Block length width depth

## Description

This package consists of commands to generate pseudo-random number generators. These new commands deliver

- numbers that are distributed normally, uniformly, according to a Pareto or Gumbel distribution and so on

- coordinates of points uniformly spread inside a sphere or a rectangle

For example:

        set p [::simulation::random::prng_Normal -1.0 10.0]

produces a new command (whose name is stored in the variable "p") that generates normally distributed numbers with a mean of -1.0 and a standard deviation of 10.0.

## PROCEDURES

The package defines the following public procedures for discrete distributions:

::simulation::random::prng_Bernoulli p

  Create a command (PRNG) that generates numbers with a Bernoulli distribution: the value is either 1 or 0, with a chance p to be 1

  float p

    Chance the outcome is 1

::simulation::random::prng_Discrete n

  Create a command (PRNG) that generates numbers 0 to n-1 with equal probability.

  int n

    Number of different values (ranging from 0 to n-1)

::simulation::random::prng_Poisson lambda

  Create a command (PRNG) that generates numbers according to the Poisson distribution.

  float lambda

    Mean number per time interval

The package defines the following public procedures for continuous distributions:

::simulation::random::prng_Uniform min max

  Create a command (PRNG) that generates uniformly distributed numbers between "min" and "max".

  float min

    Minimum number that will be generated

  float max

    Maximum number that will be generated

::simulation::random::prng_Triangular min max

  Create a command (PRNG) that generates triangularly distributed numbers between "min" and "max". If the argument min is lower than the argument max, then smaller values have higher probability and vice versa. In the first case the probability density function is of the form f(x) = 2(1-x) and the other case it is of the form f(x) = 2x.

  float min

    Minimum number that will be generated

  float max

    Maximum number that will be generated

::simulation::random::prng_SymmTriangular min max

  Create a command (PRNG) that generates numbers distributed according to a symmetric triangle around the mean of "min" and "max".

  float min

    Minimum number that will be generated

  float max

    Maximum number that will be generated

::simulation::random::prng_Exponential min mean

  Create a command (PRNG) that generates exponentially distributed numbers with a given minimum value and a given mean value.

  float min

    Minimum number that will be generated

  float mean

    Mean value for the numbers

::simulation::random::prng_Normal mean stdev

  Create a command (PRNG) that generates normally distributed numbers with a given mean value and a given standard deviation.

  float mean

    Mean value for the numbers

  float stdev

    Standard deviation

::simulation::random::prng_Pareto min steep

  Create a command (PRNG) that generates numbers distributed according to Pareto with a given minimum value and a given distribution steepness.

  float min

    Minimum number that will be generated

  float steep

    Steepness of the distribution

::simulation::random::prng_Gumbel min f

  Create a command (PRNG) that generates numbers distributed according to Gumbel with a given minimum value and a given scale factor. The probability density function is:

           P(v) = exp( -exp(f*(v-min)))

  float min

    Minimum number that will be generated

  float f

    Scale factor for the values

::simulation::random::prng_chiSquared df

  Create a command (PRNG) that generates numbers distributed according to the chi-squared distribution with df degrees of freedom. The mean is 0 and the standard deviation is 1.

  float df

    Degrees of freedom

The package defines the following public procedures for random point sets:

::simulation::random::prng_Disk rad

  Create a command (PRNG) that generates (x,y)-coordinates for points uniformly spread over a disk of given radius.

  float rad

    Radius of the disk

::simulation::random::prng_Sphere rad

  Create a command (PRNG) that generates (x,y,z)-coordinates for points uniformly spread over the surface of a sphere of given radius.

  float rad

    Radius of the disk

::simulation::random::prng_Ball rad

  Create a command (PRNG) that generates (x,y,z)-coordinates for points uniformly spread within a ball of given radius.

  float rad

    Radius of the ball

::simulation::random::prng_Rectangle length width

  Create a command (PRNG) that generates (x,y)-coordinates for points uniformly spread over a rectangle.

  float length

    Length of the rectangle (x-direction)

  float width

    Width of the rectangle (y-direction)

::simulation::random::prng_Block length width depth

  Create a command (PRNG) that generates (x,y,z)-coordinates for points uniformly spread over a block

  float length

    Length of the block (x-direction)

  float width

    Width of the block (y-direction)

  float depth

    Depth of the block (z-direction)

## Keywords

math, random numbers, simulation, statistical distribution

## Category

Mathematics

## Copyright

Copyright © 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>