Download A small note on Using Mathematica 6 to generate random variables

A small note on Using Mathematica 6 to generate
random variables that are distributed with specific
probability density
by Nasser Abbasi 8/30/076
The problem : We want to generate a set of random variables such that they fit a specific
probability distribution. Examples are shown how to do this using Mathematica 6
The method is simple. We Wrap the specific probability distribution function with the
function RandomReal or RandomInterger. Use histogram to plot the frequency distribution
of the resulting random numbers. Below are 3 examples to illustrate the method.
example 1 : Generate random numbers which are distributed normally with zero mean and
variance of 1. Generate 1000 random numbers and display histogram
In[134]:=
Needs@"Histograms`"D
t = Table@RandomReal@NormalDistribution@0, 1DD, 8i, 1000<D;
Histogram@t, PlotLabel ® "frequency of random numbers distributed normally",
AxesLabel ® 8"x", "frequency"<D
frequency of random numbers distributed normally
frequency
100
80
Out[136]=
60
40
20
-2
x
0
2
Printed by Mathematica for Students
2
nmaGenerateRandom.nb
example 2 : Generate random numbers which are distributed exponentially with parameter Λ=1.
Generate 1000 random numbers and display histogram
t = Table@RandomReal@ExponentialDistribution@1DD, 8i, 1000<D;
Histogram@t, PlotLabel ® "frequency of random numbers distributed exponentially",
AxesLabel ® 8"x", "frequency"<D
frequency of random numbers distributed exponentialy
frequency
200
150
Out[140]=
100
50
x
2
4
6
8
Printed by Mathematica for Students
nmaGenerateRandom.nb
example 3 : Generate random numbers which are distributed with Gamma Distribution with
shape parameter 2 and scaleparameter 5. Generate 1000 random numbers and display
histogram
In[145]:=
t = Table@RandomReal@GammaDistribution@2, 5DD, 8i, 1000<D;
Histogram@t, PlotLabel ® "frequency of random numbers distributed Gamma",
AxesLabel ® 8"x", "frequency"<D
frequency of random numbers distributed Gamma
frequency
140
120
100
Out[146]=
80
60
40
20
x
10
20
30
40
50
Printed by Mathematica for Students
3