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simulation::random

Pseudo-random number generators

literal type exactly as shown argument replace with your value ~~?optional?~~ may be omitted

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)

Category#

Mathematics

Copyright#

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

Keywords#

math · random numbers · simulation · statistical distribution