simulation::random(3tcl)

NAME
simulation::random - Pseudo-random number generators

SYNOPSIS
package require Tcl ?8.5 9?

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 (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>