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Name

xrandom - Return seed for random numbers and optionally random numbers

Synopsis

xrandom [parameter=value]

Description

xrandom returns a seed that can be used to random number generators, and optionally random numbers drawn from a uniform or gaussian (normal) distribution. Uniform numbers are between 0 and 1, gaussian numbers have a mean of 0 and a dispersion of 1.

If compiled with GSL, random number generator types can be selected, as well as many more distribution types.

Parameters

The following parameters are recognized in any order if the keyword is also given:
seed=
Initial seed. Use 0 for the current time (seconds since 1970.00, see also time(2) ) -1 for the number of centiseconds since boot (see times(2) ) and 2 for the current pid (see getpid(2) ). If GSL is implemented the seed value can be optionally followed by the random number generator type (default: mt19937). See xrandom(3) for more details. n= Number of random numbers to draw [Default: 0].
m=
Number of times to repeat the experiment. If more than 1, tabulating is turned off, and reporting is now doine at the end of all tests, and the statistics of the mean’s from each n sample is shown. [Default: 1].
gauss=
Return gaussian numbers instead of uniform? [Default: f]
report=
Report mean/dispersion/skewness/kurtosis? [Default: f]
tab=t|f
Tabulate all random numbers [t]
offset=
Offset of distribution from 0. Default: 0.0
gsl=
Name of the random number distribution requested. They follow the name convention of the same-name functions gsl_random_xxx in the gsl(3) library. No default.
pars=
Parameters belonging to the selected gsl name. They need to match exactly (0, 1, 2 or 3 currently). No default.

Examples

Here is an example script, grandom.csh, to test if the error in the mean scales as 1/sqrt(N):
#! /bin/csh -f
#
#       n1: sample size 
#       n2: number of times to do the experiment
set n1=100
set n2=100
foreach i (‘nemoinp 1:$n2‘)
  set log=(‘xrandom -1 100 t | tail +2 | tabhist - tab=t |& grep ^Mean‘)
  echo $log[5]
end
This script outputs n2 numbers, of which the mean should be 0 and the dispersion (now the error in the mean) 1/sqrt(n2), where 0 and 1 are the mean and dispersion of a random gaussian number from grandom(3NEMO) :
       % grandom.csh | tabhist -
100 values read
min and max value in column 1: [-0.335527 : 0.348629]
Number of points     : 100
Mean and dispersion  : 0.0120416 0.102367
Skewness and kurtosis: -0.0528344 1.19066
Median               : 0.000425562

Gsl

If the GNU Scientific Library (GSL) has been enabled during installation, the gsl= and pars keyword will appear in the keyword list of xrandom. The following random number distribution names are implemented, and the names of their parameters. Note that the number of parameters, as given in pars= has to match exactly, there are no defaults.
gaussian               sigma
gaussian_ratio_method  sigma
gaussian_tail          a sigma
exponential            mu
laplace                a
exppow                 a b
cauchy                 a
rayleigh               sigma
rayleigh_tail          a sigma
landau                 N/A   
levy                   c alpha
levy_skey              c alpha beta
gamma                  a b
flat                   a b
lognormal              zeta sigma
chisq                  nu
fdist                  nu1 nu2
tdist                  nu
beta                   a b
logistic               a
pareto                 a b
weibull                a b
gumbel1                a b
gumbel2                a b
The following functions are discrete random number distributions, and return integers:
poisson                mu
bernoulli              p
binomial               p n
negative_binomial      p n
pascal                 p k
geometric              p
hypergeometric         n1 n2 nt
logarithmic            sigma

Author

Peter Teuben

Update History


26-Nov-96    V1.0 turned TESTBED into a TOOLBOX program    PJT
13-apr-97    example
8-sep-01    V2.0 GSL optionally added    PJT
9-oct-2012    V2.2 added m=    PJT


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