# Tcl Library Source Code

Documentation Bounty program for improvements to Tcl and certain Tcl packages.

# NAME

simulation::random - Pseudo-random number generators

# SYNOPSIS

package require Tcl ?8.4?
package require simulation::random 0.4

# 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:

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,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