Page 102 - Computational Statistics Handbook with MATLAB

Chapter 4: Generating Random Variables 89

1. Generate a variate Y from the discrete uniform density on 1 … 5, , .
(One could use the MATLAB Statistics Toolbox function unidrnd
or csdunrnd.)
2. Generate a uniform random number U.
3. If

p p p
U ≤ -------- = ------------------------- = ---------- ,
Y
Y
Y
⁄
⋅
1.65 1 5 0.33
cq Y
then deliver X = Y , else return to step 1.
The implementation of this example in MATLAB is left as an exercise.

4.3 Generating Continuous Random Variables

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No
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The main MATLAB program has a function that will generate numbers from
the standard normal distribution, so we do not discuss any techniques for
generating random variables from the normal distribution. For the reader
who is interested in how normal random variates can be generated, most of
the references provided in Section 4.6 contain this information.
The MATLAB function for generating standard normal random variables
is called randn, and its functionality is similar to the function rand that was
discussed in the previous section. As with the uniform random variable U,
we can obtain a normal random variable X with mean and variance σ 2 by
µ
means of a transformation. Letting Z represent a standard normal random
variable (possibly generated from randn), we get the desired X from the rela-
tionship
⋅
X = Z σ + . µ (4.8)

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ii
Expon
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nn
butiobutio
The inverse transform method can be used to generate random variables
from the exponential distribution and serves as an example of this procedure.
The distribution function for an exponential random variable with parameter
λ is given by
© 2002 by Chapman & Hall/CRC