DMelt:Numeric/2 Random Numbers

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Random numbers

Read Random_numbers article. The DMelt random numbers can be constructed using several approaches:

The Native Java approach

Random numbers provided by Java API have already been used in the can be used to generate a single random number. Below we check the methods of this class: 

from java.util import *
r=Random()     # seed from the system time.
r=Random(100L) # user defined seed=100L
dir(r)

You will see the methods of the Random class: 

[.. 'nextDouble', 'nextFloat', 'nextGaussian',
    ...'nextInt', 'nextLong' ..]

Here is an example of how to fill a list with Gaussian random numbers: 

from java.util import *
r=Random()
g=[]
for i in range(100):
   g.append(r.nextGaussian())

The Native Python approach

Let us give a simple example which shows how to generate a single random floating point number in the range [0,1] using the Python API: 

from random import *
r=Random()
a=r.randint(1,10) # a random number in range [0.10]

A random seed from the current system time is used since we do not specify any argument for the Random(). In order to generate a random number predictably for debugging purpose, one should pass an integer (or long) value to the Random(), i.e., for example Random(1L).

One can use the following random number methods: 

*  r.random()            # in range [0.0, 1.0)
*  r.randint(min,max)    # int in range [min,max] 
*  r.uniform(min,max)    # real number in [min,max]
*  r.betavariate(a,b)    # Beta distribution (a>0,b>0)
*  r.expovariate(lambda) # Exponential distribution
*  r.gauss(m,s)          # Gaussian distribution with the mean "m" and sigma "s"
*  r.lognormvariate(m,s) # Log normal distribution with the mean "m" and sigma "s"
*  r.normalvariate(m,s)  # Normal distribution with the mean "m" and sigma "s"
*  r.gammavariate(a, b) # Gamma distribution.
*  r.seed(i)             # set seed (i integer or long)
*  state=r.getstate()    # returns internal state
*  setstate(state)       # restores internal st


Random numbers are also used for manipulations with lists. One can randomly rearrange elements in a list as: 

list=[1,2,3,4,5,6,7,8,9]
r.shuffle(list)
print list

The code generates this: 

[3, 4, 2, 7, 6, 5, 9, 8, 1]

The Native DataMelt approach

Use the package "cern.jet.random" to build random numbers in DataMelt. Check this out as: 

import cern.jet.random
 dir(cern.jet.random)

This will printout the available classes for generation of random distributions: 

Beta, Binomial, BreitWigner, BreitWignerMeanSquare,
ChiSquare, Empirical, EmpiricalWalker, Exponential,
ExponentialPower, Gamma, Hyperbolic, HyperGeometric,
Logarithmic, NegativeBinomial, Normal, Poisson,
PoissonSlow, StudentT, Uniform, VonMises, Zeta

Let us give an example how to generate 100 integer values distributed in accordance with a Poissonian distribution (with the mean 10) 

from cern.jet.random.engine import *
from cern.jet.random  import *
engine=MersenneTwister()
poisson=Poisson(10,engine)
for i in range(100):
      print  poisson.nextInt()

The MersenneTwister is one of the strongest engines. One can use the current system date for a seed to avoid reproducible random numbers: 

from cern.jet.random.engine import *
 import java
 engine=MersenneTwister(new java.util.Date())

Distributions from density functions

Here is a code example showing how to generate random distribution from any given function. Read more deatils in jhplot.math.StatisticSample jhplot.math.StatisticSample. 

from jhplot  import *
from jhplot.math.StatisticSample  import *
from java.awt import *

c1 = HPlot('Canvas',600,400)
c1.setGTitle('Title')
c1.visible()
c1.setRange(-1,11,0,30)

f=F1D('10+2*cos(x)',0,10)
f.setColor(Color.red)
c1.draw(f)
p=f.getParse()

a=randomRejection(1000,p,15,0,10)
h=H1D('Random numbers',100,0,10)
h.fill(a)
c1.draw(h)

Third-party libraries

DataMelt contains a number of third-party Java libraries that can be used for computation of density (PDF), cumulative (CDF), quantile, and random variates of many popular statistical distributions, such as:

  • Ansari-Bradley
  • Beta
  • Binomial
  • Cauchy
  • Chi square
  • Exponential
  • Fisher's F
  • Gamma
  • Geometric
  • Hypergeometric
  • Kendall
  • Logistic
  • Log normal
  • Negative binomial
  • Non-central beta,
  • Non-central chi square,
  • Non-central F
  • Non-central T
  • Normal
  • Poisson
  • Sign rank
  • Spearman
  • Student's T
  • Tukey
  • Uniform
  • Weibull
  • Wilcoxon

and many others. Here is the list you can access and include into your programs. Look at the following Java packages:

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