simulation::random - Pseudo-random number generators

       Mathematics

       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>

tcllib                                                 0.4                              simulation::random(3tcl)

       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.

       math, random numbers, simulation, statistical distribution

       simulation::random - Pseudo-random number generators

       The package defines the following public procedures for discrete distributions:

       ::simulation::random::prng_Bernoullip
              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_Discreten
              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_Poissonlambda
              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_Uniformminmax
              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_Triangularminmax
              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_SymmTriangularminmax
              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_Exponentialminmean
              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_Normalmeanstdev
              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_Paretominsteep
              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_Gumbelminf
              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_chiSquareddf
              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_Diskrad
              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_Sphererad
              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_Ballrad
              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_Rectanglelengthwidth
              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_Blocklengthwidthdepth
              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)

       package require Tcl?8.59?

       package require simulation::random0.4::simulation::random::prng_Bernoullip::simulation::random::prng_Discreten::simulation::random::prng_Poissonlambda::simulation::random::prng_Uniformminmax::simulation::random::prng_Triangularminmax::simulation::random::prng_SymmTriangularminmax::simulation::random::prng_Exponentialminmean::simulation::random::prng_Normalmeanstdev::simulation::random::prng_Paretominsteep::simulation::random::prng_Gumbelminf::simulation::random::prng_chiSquareddf::simulation::random::prng_Diskrad::simulation::random::prng_Sphererad::simulation::random::prng_Ballrad::simulation::random::prng_Rectanglelengthwidth::simulation::random::prng_Blocklengthwidthdepth

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