 simulation::random(3) 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_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:

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

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

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

::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)-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 (c) 2004 Arjen Markus <[email protected]>