'\"
'\" Generated from file 'simulation_random\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>
'\"
.TH "simulation::random" n 0\&.4 tcllib "Tcl Simulation Tools"
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.BS
.SH NAME
simulation::random \- Pseudo-random number generators
.SH SYNOPSIS
package require \fBTcl  ?8\&.4?\fR
.sp
package require \fBsimulation::random  0\&.4\fR
.sp
\fB::simulation::random::prng_Bernoulli\fR \fIp\fR
.sp
\fB::simulation::random::prng_Discrete\fR \fIn\fR
.sp
\fB::simulation::random::prng_Poisson\fR \fIlambda\fR
.sp
\fB::simulation::random::prng_Uniform\fR \fImin\fR \fImax\fR
.sp
\fB::simulation::random::prng_Triangular\fR \fImin\fR \fImax\fR
.sp
\fB::simulation::random::prng_SymmTriangular\fR \fImin\fR \fImax\fR
.sp
\fB::simulation::random::prng_Exponential\fR \fImin\fR \fImean\fR
.sp
\fB::simulation::random::prng_Normal\fR \fImean\fR \fIstdev\fR
.sp
\fB::simulation::random::prng_Pareto\fR \fImin\fR \fIsteep\fR
.sp
\fB::simulation::random::prng_Gumbel\fR \fImin\fR \fIf\fR
.sp
\fB::simulation::random::prng_chiSquared\fR \fIdf\fR
.sp
\fB::simulation::random::prng_Disk\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Sphere\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Ball\fR \fIrad\fR
.sp
\fB::simulation::random::prng_Rectangle\fR \fIlength\fR \fIwidth\fR
.sp
\fB::simulation::random::prng_Block\fR \fIlength\fR \fIwidth\fR \fIdepth\fR
.sp
.BE
.SH DESCRIPTION
.PP
This package consists of commands to generate pseudo-random number
generators\&. These new commands deliver
.IP \(bu
numbers that are distributed normally, uniformly, according to a
Pareto or Gumbel distribution and so on
.IP \(bu
coordinates of points uniformly spread inside a sphere or a rectangle
.PP
For example:
.CS


    set p [::simulation::random::prng_Normal -1\&.0 10\&.0]

.CE
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\&.
.SH PROCEDURES
The package defines the following public procedures for \fIdiscrete\fR
distributions:
.TP
\fB::simulation::random::prng_Bernoulli\fR \fIp\fR
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
.RS
.TP
float \fIp\fR
Chance the outcome is 1
.RE
.sp
.TP
\fB::simulation::random::prng_Discrete\fR \fIn\fR
Create a command (PRNG) that generates numbers 0 to n-1 with equal
probability\&.
.RS
.TP
int \fIn\fR
Number of different values (ranging from 0 to n-1)
.RE
.sp
.TP
\fB::simulation::random::prng_Poisson\fR \fIlambda\fR
Create a command (PRNG) that generates numbers according to the Poisson
distribution\&.
.RS
.TP
float \fIlambda\fR
Mean number per time interval
.RE
.PP
The package defines the following public procedures for \fIcontinuous\fR distributions:
.TP
\fB::simulation::random::prng_Uniform\fR \fImin\fR \fImax\fR
Create a command (PRNG) that generates uniformly distributed numbers
between "min" and "max"\&.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImax\fR
Maximum number that will be generated
.RE
.sp
.TP
\fB::simulation::random::prng_Triangular\fR \fImin\fR \fImax\fR
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 \fIf(x) = 2(1-x)\fR and the other case it is of the form \fIf(x) = 2x\fR\&.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImax\fR
Maximum number that will be generated
.RE
.sp
.TP
\fB::simulation::random::prng_SymmTriangular\fR \fImin\fR \fImax\fR
Create a command (PRNG) that generates numbers distributed according to a symmetric triangle
around the mean of "min" and "max"\&.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImax\fR
Maximum number that will be generated
.RE
.sp
.TP
\fB::simulation::random::prng_Exponential\fR \fImin\fR \fImean\fR
Create a command (PRNG) that generates exponentially distributed numbers
with a given minimum value and a given mean value\&.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fImean\fR
Mean value for the numbers
.RE
.sp
.TP
\fB::simulation::random::prng_Normal\fR \fImean\fR \fIstdev\fR
Create a command (PRNG) that generates normally distributed numbers
with a given mean value and a given standard deviation\&.
.RS
.TP
float \fImean\fR
Mean value for the numbers
.TP
float \fIstdev\fR
Standard deviation
.RE
.sp
.TP
\fB::simulation::random::prng_Pareto\fR \fImin\fR \fIsteep\fR
Create a command (PRNG) that generates numbers distributed according to
Pareto with a given minimum value and a given distribution steepness\&.
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fIsteep\fR
Steepness of the distribution
.RE
.sp
.TP
\fB::simulation::random::prng_Gumbel\fR \fImin\fR \fIf\fR
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:
.CS


     P(v) = exp( -exp(f*(v-min)))

.CE
.RS
.TP
float \fImin\fR
Minimum number that will be generated
.TP
float \fIf\fR
Scale factor for the values
.RE
.sp
.TP
\fB::simulation::random::prng_chiSquared\fR \fIdf\fR
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\&.
.RS
.TP
float \fIdf\fR
Degrees of freedom
.RE
.PP
The package defines the following public procedures for random point sets:
.TP
\fB::simulation::random::prng_Disk\fR \fIrad\fR
Create a command (PRNG) that generates (x,y)-coordinates for points
uniformly spread over a disk of given radius\&.
.RS
.TP
float \fIrad\fR
Radius of the disk
.RE
.sp
.TP
\fB::simulation::random::prng_Sphere\fR \fIrad\fR
Create a command (PRNG) that generates (x,y,z)-coordinates for points
uniformly spread over the surface of a sphere of given radius\&.
.RS
.TP
float \fIrad\fR
Radius of the disk
.RE
.sp
.TP
\fB::simulation::random::prng_Ball\fR \fIrad\fR
Create a command (PRNG) that generates (x,y,z)-coordinates for points
uniformly spread within a ball of given radius\&.
.RS
.TP
float \fIrad\fR
Radius of the ball
.RE
.sp
.TP
\fB::simulation::random::prng_Rectangle\fR \fIlength\fR \fIwidth\fR
Create a command (PRNG) that generates (x,y)-coordinates for points
uniformly spread over a rectangle\&.
.RS
.TP
float \fIlength\fR
Length of the rectangle (x-direction)
.TP
float \fIwidth\fR
Width of the rectangle (y-direction)
.RE
.sp
.TP
\fB::simulation::random::prng_Block\fR \fIlength\fR \fIwidth\fR \fIdepth\fR
Create a command (PRNG) that generates (x,y,z)-coordinates for points
uniformly spread over a block
.RS
.TP
float \fIlength\fR
Length of the block (x-direction)
.TP
float \fIwidth\fR
Width of the block (y-direction)
.TP
float \fIdepth\fR
Depth of the block (z-direction)
.RE
.PP
.SH KEYWORDS
math, random numbers, simulation, statistical distribution
.SH CATEGORY
Mathematics
.SH COPYRIGHT
.nf
Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>

.fi