Page 123 - Computational Statistics Handbook with MATLAB

110 Computational Statistics Handbook with MATLAB

4.9. Run Example 4.4 and generate 500 random variables. Plot a histogram
of the variates. Does it match the probability density function shown
in Figure 4.3?
4.10. Implement Example 4.5 in MATLAB. Generate 100 random variables.
What is the relative frequency of each value of the random variable
,
,
1 … 5 ? Does this match the probability mass function?
,,
,
4.11. Generate four sets of random variables with ν = 25 15 20, using
the function cschirnd. Create histograms for each sample. How does
ν
the shape of the distribution depend on the degrees of freedom ?
4.12. Repeat Example 4.13 for larger sample sizes. Is the agreement better
between the observed relative frequencies and the theoretical values?
4.13. Generate 1000 binomial random variables for n = 5 and
,
,
p = 0.3 0.5 0.8. In each case, determine the observed relative fre-
quencies and the corresponding theoretical probabilities. How is the
agreement between them?
4.14. The MATLAB Statistics Toolbox has a GUI called randtool. This
is an interactive demo that generates random variables from distri-
butions that are available in the toolbox. The user can change param-
eter values and see the results via a histogram. There are options to
change the sample size and to output the results. To start the GUI,
simply type randtool at the command line. Run the function and
experiment with the distributions that are discussed in the text (nor-
mal, exponential, gamma, beta, etc.).
4.15. The plot on the right in Figure 4.6 shows a histogram of beta random
variables with parameters α = β = 0.5 . Construct a similar plot
using the information in Example 4.9.

© 2002 by Chapman & Hall/CRC