Page 113 - Computational Statistics Handbook with MATLAB

100 Computational Statistics Handbook with MATLAB

Example 4.11
The following function cssphrnd generates random variables on a d-dimen-
sional unit sphere. We illustrate its use by generating random variables that
are on the unit circle S 2 .
% function X = cssphrnd(n,d);
% This function will generate n d-dimensional
% random variates that are distributed on the
% unit d-dimensional sphere. d >= 2

function X = cssphrnd(n,d)
if d < 2
error('ERROR - d must be greater than 1.')
break
end
% Generate standard normal random variables.
tmp = randn(d,n);
% Find the magnitude of each column.
% Square each element, add and take the square root.
mag = sqrt(sum(tmp.^2));
% Make a diagonal matrix of them - inverses.
dm = diag(1./mag);
% Multiply to scale properly.
% Transpose so X contains the observations.
X = (tmp*dm)';

We can use this function to generate a set of random variables for d = 2 and
plot the result in Figure 4.8.
X = cssphrnd(500,2);
plot(X(:,1),X(:,2),'x')
axis equal
xlabel('X_1'),ylabel('X_2')

4.4 Generating Discrete Random Variables

Binomia l ll
BinomiaBinomia
Binomia
l
A binomial random variable with parameters n and p represents the number
of successes in n independent trials. We can obtain a binomial random vari-
© 2002 by Chapman & Hall/CRC