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simulation::random(n) Tcl Simulation Tools simulation::random(n) 





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










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







  

  
Chance the outcome is 1









  
::simulation::random::prng_Discrete n

  
Create a command (PRNG) that generates numbers 0 to n-1 with equal
      probability.







  

  
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.







  

  
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".







  

  
Minimum number that will be generated

  

  
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.







  

  
Minimum number that will be generated

  

  
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".







  

  
Minimum number that will be generated

  

  
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.







  

  
Minimum number that will be generated

  

  
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.







  

  
Mean value for the numbers

  

  
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.







  

  
Minimum number that will be generated

  

  
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)))








  

  
Minimum number that will be generated

  

  
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.







  

  
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.







  

  
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.







  

  
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.







  

  
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.







  

  
Length of the rectangle (x-direction)

  

  
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







  

  
Length of the block (x-direction)

  

  
Width of the block (y-direction)

  

  
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>








  

    0.4
    tcllib