Added exercises for mle

statistics/code/mlemean.m

@@ -1,5 +1,5 @@
 % draw random numbers:
-n = 500;
+n = 100;
 mu = 3.0;
 sigma =2.0;
 x = randn(n,1)*sigma+mu;
@@ -19,33 +19,11 @@ lm = prod(lms, 1);          % likelihood
 loglm = sum(log(lms), 1);   % log likelihood
 
 % plot likelihood of mean:
-subplot(2, 2, 1);
+subplot(1, 2, 1);
 plot(pmus, lm );
 xlabel('mean')
 ylabel('likelihood')
-subplot(2, 2, 2);
+subplot(1, 2, 2);
 plot(pmus, loglm );
 xlabel('mean')
 ylabel('log likelihood')
-
-% standard deviation as parameter:
-psigs = 1.0:0.01:3.0;
-% matrix with the probabilities for each x and psigs:
-lms = zeros(length(x), length(psigs));
-for i=1:length(psigs)
-    psig = psigs(i);
-    p = exp(-0.5*((x-mu)/psig).^2.0)/sqrt(2.0*pi)/psig;
-    lms(:,i) = p;
-end
-lm = prod(lms, 1);          % likelihood
-loglm = sum(log(lms), 1);   % log likelihood
-
-% plot likelihood of standard deviation:
-subplot(2, 2, 3);
-plot(psigs, lm );
-xlabel('standard deviation')
-ylabel('likelihood')
-subplot(2, 2, 4);
-plot(psigs, loglm);
-xlabel('standard deviation')
-ylabel('log likelihood')

statistics/code/mlepdffit.m

@@ -1,27 +0,0 @@
-% plot gamma pdfs:
-xx = 0.0:0.1:10.0;
-shapes = [ 1.0, 2.0, 3.0, 5.0];
-cc = jet(length(shapes) );
-for i=1:length(shapes)
-    yy = gampdf(xx, shapes(i), 1.0);
-    plot(xx, yy, '-', 'linewidth', 3, 'color', cc(i,:), ...
-        'DisplayName', sprintf('s=%.0f', shapes(i)) );
-    hold on;
-end
-
-% generate gamma distributed random numbers:
-n = 50;
-x = gamrnd(3.0, 1.0, n, 1);
-
-% histogram:
-[h,b] = hist(x, 15);
-h = h/sum(h)/(b(2)-b(1));
-bar(b, h, 1.0, 'DisplayName', 'data');
-
-% maximum likelihood estimate:
-p = mle(x, 'distribution', 'gamma');
-yy = gampdf(xx, p(1), p(2));
-plot(xx, yy, '-k', 'linewidth', 5, 'DisplayName', 'mle' );
-
-hold off;
-legend('show');

statistics/code/mlepropfit.m

@@ -1,29 +0,0 @@
-m = 2.0;      % slope
-sigma = 1.0;  % standard deviation
-n = 100;      % number of data pairs
-
-% data pairs:
-x = 5.0*rand(n, 1);
-y = m*x + sigma*randn(n, 1);
-
-% fit:
-slope = mleslope(x, y);
-fprintf('slopes:\n');
-fprintf('original = %.2f\n', m);
-fprintf('     fit = %.2f\n', slope);
-
-% lines:
-xx = 0.0:0.1:5.0;     % x-axis values
-yorg = m*xx;
-yfit = slope*xx;
-
-% plot:
-plot(xx, yorg, '-r', 'linewidth', 5);
-hold on;
-plot(xx, yfit, '-g', 'linewidth', 2);
-plot(x, y, 'ob');
-hold off;
-legend('data', 'original', 'fit', 'Location', 'NorthWest');
-legend('boxoff')
-xlabel('x');
-ylabel('y');

statistics/code/mleslope.m

@@ -1,6 +0,0 @@
-function slope = mleslope(x, y )
-% Compute the maximum likelihood estimate of the slope
-% of a line through the origin 
-% given the data pairs in the vectors x and y.
-    slope = sum(x.*y)/sum(x.*x);
-end