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

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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

       o      numbers that are distributed normally, uniformly, according to a Pareto or Gumbel distribution and so on

       o      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)-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

COPYRIGHT

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

simulation								0.1						     simulation::random(n)