NAME

       simulation::random - 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_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_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>