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  0.4
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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_Triangular min max
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25       ::simulation::random::prng_SymmTriangular min max
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27       ::simulation::random::prng_Exponential min mean
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29       ::simulation::random::prng_Normal mean stdev
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31       ::simulation::random::prng_Pareto min steep
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33       ::simulation::random::prng_Gumbel min f
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35       ::simulation::random::prng_chiSquared df
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37       ::simulation::random::prng_Disk rad
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39       ::simulation::random::prng_Sphere rad
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41       ::simulation::random::prng_Ball rad
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43       ::simulation::random::prng_Rectangle length width
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45       ::simulation::random::prng_Block length width depth
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DESCRIPTION

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

69       The package defines the following public procedures for  discrete  dis‐
70       tributions:
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72       ::simulation::random::prng_Bernoulli p
73              Create  a command (PRNG) that generates numbers with a Bernoulli
74              distribution: the value is either 1 or 0, with a chance p to  be
75              1
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77              float p
78                     Chance the outcome is 1
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80
81       ::simulation::random::prng_Discrete n
82              Create  a  command  (PRNG)  that generates numbers 0 to n-1 with
83              equal probability.
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85              int n  Number of different values (ranging from 0 to n-1)
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87
88       ::simulation::random::prng_Poisson lambda
89              Create a command (PRNG) that generates numbers according to  the
90              Poisson distribution.
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92              float lambda
93                     Mean number per time interval
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95       The package defines the following public procedures for continuous dis‐
96       tributions:
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98       ::simulation::random::prng_Uniform min max
99              Create a command (PRNG)  that  generates  uniformly  distributed
100              numbers between "min" and "max".
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102              float min
103                     Minimum number that will be generated
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105              float max
106                     Maximum number that will be generated
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108
109       ::simulation::random::prng_Triangular min max
110              Create  a command (PRNG) that generates triangularly distributed
111              numbers between "min" and "max". If the argument  min  is  lower
112              than the argument max, then smaller values have higher probabil‐
113              ity and vice versa. In the first case  the  probability  density
114              function  is  of the form f(x) = 2(1-x) and the other case it is
115              of the form f(x) = 2x.
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117              float min
118                     Minimum number that will be generated
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120              float max
121                     Maximum number that will be generated
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124       ::simulation::random::prng_SymmTriangular min max
125              Create a command (PRNG) that generates numbers  distributed  ac‐
126              cording  to  a  symmetric  triangle around the mean of "min" and
127              "max".
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129              float min
130                     Minimum number that will be generated
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132              float max
133                     Maximum number that will be generated
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135
136       ::simulation::random::prng_Exponential min mean
137              Create a command (PRNG) that generates exponentially distributed
138              numbers with a given minimum value and a given mean value.
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140              float min
141                     Minimum number that will be generated
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143              float mean
144                     Mean value for the numbers
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146
147       ::simulation::random::prng_Normal mean stdev
148              Create a command (PRNG) that generates normally distributed num‐
149              bers with a given mean value and a given standard deviation.
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151              float mean
152                     Mean value for the numbers
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154              float stdev
155                     Standard deviation
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157
158       ::simulation::random::prng_Pareto min steep
159              Create a command (PRNG) that generates numbers  distributed  ac‐
160              cording to Pareto with a given minimum value and a given distri‐
161              bution steepness.
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163              float min
164                     Minimum number that will be generated
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166              float steep
167                     Steepness of the distribution
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170       ::simulation::random::prng_Gumbel min f
171              Create a command (PRNG) that generates numbers  distributed  ac‐
172              cording  to  Gumbel with a given minimum value and a given scale
173              factor. The probability density function is:
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175
176                   P(v) = exp( -exp(f*(v-min)))
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178
179              float min
180                     Minimum number that will be generated
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182              float f
183                     Scale factor for the values
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185
186       ::simulation::random::prng_chiSquared df
187              Create a command (PRNG) that generates numbers  distributed  ac‐
188              cording to the chi-squared distribution with df degrees of free‐
189              dom. The mean is 0 and the standard deviation is 1.
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191              float df
192                     Degrees of freedom
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194       The package defines the following public procedures  for  random  point
195       sets:
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197       ::simulation::random::prng_Disk rad
198              Create  a  command  (PRNG)  that generates (x,y)-coordinates for
199              points uniformly spread over a disk of given radius.
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201              float rad
202                     Radius of the disk
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205       ::simulation::random::prng_Sphere rad
206              Create a command (PRNG) that generates  (x,y,z)-coordinates  for
207              points  uniformly  spread  over the surface of a sphere of given
208              radius.
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210              float rad
211                     Radius of the disk
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213
214       ::simulation::random::prng_Ball rad
215              Create a command (PRNG) that generates  (x,y,z)-coordinates  for
216              points uniformly spread within a ball of given radius.
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218              float rad
219                     Radius of the ball
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221
222       ::simulation::random::prng_Rectangle length width
223              Create  a  command  (PRNG)  that generates (x,y)-coordinates for
224              points uniformly spread over a rectangle.
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226              float length
227                     Length of the rectangle (x-direction)
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229              float width
230                     Width of the rectangle (y-direction)
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233       ::simulation::random::prng_Block length width depth
234              Create a command (PRNG) that generates  (x,y,z)-coordinates  for
235              points uniformly spread over a block
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237              float length
238                     Length of the block (x-direction)
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240              float width
241                     Width of the block (y-direction)
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243              float depth
244                     Depth of the block (z-direction)
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KEYWORDS

247       math, random numbers, simulation, statistical distribution
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CATEGORY

250       Mathematics
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COPYRIGHT

253       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
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258tcllib                                0.4                simulation::random(n)