focal (3) simulation_random.3tcl.gz
NAME
simulation::random - Pseudo-random number generators
SYNOPSIS
package require Tcl ?8.4?
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
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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>