37 lines
1.0 KiB
Matlab
37 lines
1.0 KiB
Matlab
% draw random numbers:
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n = 100;
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mu = 3.0;
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sigma =2.0;
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x = randn(n,1)*sigma+mu;
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fprintf('standard deviation of the data is %.2f\n', std(x))
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fprintf(' mean of the data is %.2f\n', mean(x))
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% mean as parameter:
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pmus = 2.0:0.01:4.0;
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% matrix with the probabilities for each x and pmus:
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lms = zeros(length(x), length(pmus));
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for i=1:length(pmus)
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pmu = pmus(i);
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p = exp(-0.5*((x-pmu)/sigma).^2.0)/sqrt(2.0*pi)/sigma;
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lms(:,i) = p;
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end
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lm = prod(lms, 1); % likelihood
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loglm = sum(log(lms), 1); % log likelihood
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% position of maxima:
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maxlm = max(lm); % height of the maximum
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pmumaxlm = pmus(lm==maxlm); % pmu where lm is at maximum
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pmumaxloglm = pmus(loglm==max(loglm)); % same for loglm in one line
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fprintf(' maximum of likelihood is at %.2f\n', pmumaxlm)
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fprintf(' maximum of log-likelihood is at %.2f\n', pmumaxloglm)
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% plot likelihood of mean:
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subplot(1, 2, 1);
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plot(pmus, lm);
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xlabel('mean')
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ylabel('likelihood')
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subplot(1, 2, 2);
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plot(pmus, loglm);
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xlabel('mean')
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ylabel('log likelihood')
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