simulation::random(3tcl)

NAME
simulation::random - Pseudo-random number generators

SYNOPSIS
package require Tcl ?8.4?

package require simulation::random 0.1

::simulation::random::prng_Bernoulli p

::simulation::random::prng_Discrete n

::simulation::random::prng_Poisson lambda

::simulation::random::prng_Uniform 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_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 (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>