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Chapter 8: Probability Density Estimation 309

2. First determine the component membership of each of the n random
variables. We do this by generating n uniform (0,1) random vari-
). Component membership is determined as follows
ables (U i
If 0 ≤ U i < p 1 , then X i is from component density 1.

If p 1 ≤ U < p 1 + p 2 , then X i is from component density 2.
i
. . .
c – 1
If ∑ p j ≤ U ≤ 1 , then X i is from component density c.
i
j = 1
from the corresponding g i x;θ i ) using the compo-
(
3. Generate the X i
nent membership found in step 2.
Note that with this procedure, one could generate random variables from a
mixture of any component densities. For instance, the model could be a mix-
ture of exponentials, betas, etc.

Example 8.13
Generate a random sample of size n from a finite mixture estimate of the Old
Faithful Geyser data (geyser). First we have to load up the data and build a
finite mixture model.
load geyser
% Expects rows to be observations.
data = geyser';
% Get the finite mixture.
% Use a two term model.
% Set initial model to means at 50 and 80.
muin = [50, 80];
% Set mixing coefficients equal.
piesin = [0.5, 0.5];
% Set initial variances to 1.
varin = [1, 1];
max_it = 100;
tol = 0.001;
% Call the finite mixtures.
[pies,mus,vars]=...
csfinmix(data,muin,varin,piesin,max_it,tol);
Now generate some random variables according to this estimated model.
% Now generate some random variables from this model.
% Get the true model to generate data from this.
n = 300;
x = zeros(n,1);

© 2002 by Chapman & Hall/CRC