Updated maximum likelihood chapter.

Common latex header file.

likelihood/code/mlegammafit.m

@@ -0,0 +1,12 @@
+% generate gamma distributed random numbers:
+n = 50;
+shape = 2.0;
+scale = 1.0;
+x = gamrnd(shape, scale, n, 1);
+
+% maximum likelihood estimate:
+p = mle(x, 'distribution', 'gamma');
+
+% report results:
+fprintf('shape=%.2f\n', p(1));
+fprintf('scale=%.2f\n', p(2));

likelihood/code/mlemean.m

@@ -3,8 +3,8 @@ n = 100;
 mu = 3.0;
 sigma =2.0;
 x = randn(n,1)*sigma+mu;
-fprintf('              mean of the data is %.2f\n', mean(x))
 fprintf('standard deviation of the data is %.2f\n', std(x))
+fprintf('              mean of the data is %.2f\n', mean(x))
 
 % mean as parameter:
 pmus = 2.0:0.01:4.0;
@@ -18,12 +18,19 @@ end
 lm = prod(lms, 1);          % likelihood
 loglm = sum(log(lms), 1);   % log likelihood
 
+% position of maxima:
+maxlm = max(lm);                        % height of the maximum
+pmumaxlm = pmus(lm==maxlm);             % pmu where lm is at maximum
+pmumaxloglm = pmus(loglm==max(loglm));  % same for loglm in one line
+fprintf('      maximum of likelihood is at %.2f\n', pmumaxlm)
+fprintf('  maximum of log-likelihood is at %.2f\n', pmumaxloglm)
+
 % plot likelihood of mean:
 subplot(1, 2, 1);
-plot(pmus, lm );
+plot(pmus, lm);
 xlabel('mean')
 ylabel('likelihood')
 subplot(1, 2, 2);
-plot(pmus, loglm );
+plot(pmus, loglm);
 xlabel('mean')
 ylabel('log likelihood')