1simulation::random(n)        Tcl Simulation Tools        simulation::random(n)
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NAME

8       simulation::random - Pseudo-random number generators
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SYNOPSIS

11       package require Tcl  ?8.4?
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13       package require simulation::random  0.1
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15       ::simulation::random::prng_Bernoulli p
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17       ::simulation::random::prng_Discrete n
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19       ::simulation::random::prng_Poisson lambda
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21       ::simulation::random::prng_Uniform min max
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23       ::simulation::random::prng_Exponential min mean
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25       ::simulation::random::prng_Normal mean stdev
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27       ::simulation::random::prng_Pareto min steep
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29       ::simulation::random::prng_Gumbel min f
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31       ::simulation::random::prng_chiSquared df
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33       ::simulation::random::prng_Disk rad
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35       ::simulation::random::prng_Sphere rad
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37       ::simulation::random::prng_Ball rad
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39       ::simulation::random::prng_Rectangle length width
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41       ::simulation::random::prng_Block length width depth
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DESCRIPTION

46       This package consists of commands to generate pseudo-random number gen‐
47       erators. These new commands deliver
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49       ·      numbers that are distributed normally, uniformly, according to a
50              Pareto or Gumbel distribution and so on
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52       ·      coordinates of points uniformly spread inside a sphere or a rec‐
53              tangle
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55       For example:
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58                  set p [::simulation::random::prng_Normal -1.0 10.0]
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60       produces a new command (whose name is stored in the variable "p")  that
61       generates  normally distributed numbers with a mean of -1.0 and a stan‐
62       dard deviation of 10.0.
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PROCEDURES

65       The package defines the following public procedures for  discrete  dis‐
66       tributions:
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68       ::simulation::random::prng_Bernoulli p
69              Create  a command (PRNG) that generates numbers with a Bernoulli
70              distribution: the value is either 1 or 0, with a chance p to  be
71              1
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73              float p
74                     Chance the outcome is 1
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77       ::simulation::random::prng_Discrete n
78              Create  a  command  (PRNG)  that generates numbers 0 to n-1 with
79              equal probability.
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81              int n  Number of different values (ranging from 0 to n-1)
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84       ::simulation::random::prng_Poisson lambda
85              Create a command (PRNG) that generates numbers according to  the
86              Poisson distribution.
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88              float lambda
89                     Mean number per time interval
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91       The package defines the following public procedures for continuous dis‐
92       tributions:
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94       ::simulation::random::prng_Uniform min max
95              Create a command (PRNG)  that  generates  uniformly  distributed
96              numbers between "min" and "max".
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98              float min
99                     Minimum number that will be generated
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101              float max
102                     Maximum number that will be generated
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105       ::simulation::random::prng_Exponential min mean
106              Create a command (PRNG) that generates exponentially distributed
107              numbers with a given minimum value and a given mean value.
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109              float min
110                     Minimum number that will be generated
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112              float mean
113                     Mean value for the numbers
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116       ::simulation::random::prng_Normal mean stdev
117              Create a command (PRNG) that generates normally distributed num‐
118              bers with a given mean value and a given standard deviation.
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120              float mean
121                     Mean value for the numbers
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123              float stdev
124                     Standard deviation
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127       ::simulation::random::prng_Pareto min steep
128              Create  a  command  (PRNG)  that  generates  numbers distributed
129              according to Pareto with a given minimum value and a given  dis‐
130              tribution steepness.
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132              float min
133                     Minimum number that will be generated
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135              float steep
136                     Steepness of the distribution
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139       ::simulation::random::prng_Gumbel min f
140              Create  a  command  (PRNG)  that  generates  numbers distributed
141              according to Gumbel with a given minimum value and a given scale
142              factor. The probability density function is:
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144
145                   P(v) = exp( -exp(f*(v-min)))
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148              float min
149                     Minimum number that will be generated
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151              float f
152                     Scale factor for the values
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155       ::simulation::random::prng_chiSquared df
156              Create  a  command  (PRNG)  that  generates  numbers distributed
157              according to the chi-squared distribution  with  df  degrees  of
158              freedom. The mean is 0 and the standard deviation is 1.
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160              float df
161                     Degrees of freedom
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163       The  package  defines  the following public procedures for random point
164       sets:
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166       ::simulation::random::prng_Disk rad
167              Create a command (PRNG)  that  generates  (x,y)-coordinates  for
168              points uniformly spread over a disk of given radius.
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170              float rad
171                     Radius of the disk
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174       ::simulation::random::prng_Sphere rad
175              Create  a  command (PRNG) that generates (x,y,z)-coordinates for
176              points uniformly spread over the surface of a  sphere  of  given
177              radius.
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179              float rad
180                     Radius of the disk
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183       ::simulation::random::prng_Ball rad
184              Create  a  command (PRNG) that generates (x,y,z)-coordinates for
185              points uniformly spread within a ball of given radius.
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187              float rad
188                     Radius of the ball
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191       ::simulation::random::prng_Rectangle length width
192              Create a command (PRNG)  that  generates  (x,y)-coordinates  for
193              points uniformly spread over a rectangle.
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195              float length
196                     Length of the rectangle (x-direction)
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198              float width
199                     Width of the rectangle (y-direction)
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202       ::simulation::random::prng_Block length width depth
203              Create  a  command (PRNG) that generates (x,y,z)-coordinates for
204              points uniformly spread over a block
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206              float length
207                     Length of the block (x-direction)
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209              float width
210                     Width of the block (y-direction)
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212              float depth
213                     Depth of the block (z-direction)
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KEYWORDS

216       math, random numbers, simulation, statistical distribution
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CATEGORY

219       Mathematics
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COPYRIGHT

222       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
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227tcllib                                0.1                simulation::random(n)