# Tcl Library Source Code

simulation::random - Tcl Simulation Tools
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# simulation::random(n) 0.1 tcllib "Tcl Simulation Tools"

## Name

simulation::random - Pseudo-random number generators

## 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.

Radius of the disk

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

Radius of the disk

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

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)

Mathematics