# Maximum likelihood estimators

This applet shows the (log of the) likelihood function, and the maximum likelihood estimator, for a sample and various statistical models.

This applet demonstrates the principle of maximum likelihood estimation.

The blue curve represents a possible population generating the data, with parameter θ. You can change population types by using the buttons at top-right.

An actual observed sample *x*_{1}, *x*_{2}, … is shown along the horizontal axis. You can adjust the sample size n using the slider at the top-left. You can move individual sample observations by dragging them. The likelihood of each *x*_{i} for the current θ value is shown as a dotted blue line.

You can drag the blue point to adjust θ, and observe how the likelihoods of the sample points are affected. You can also key in a new value for θ in the text box. Try to guess the MLE by dragging θ and observing the likelihoods, particularly for sample sizes 1 and 2.

You can show the likelihood of the whole sample, and the MLE, using the 'Likelihood function' checkbox. You can switch to the log-likelihood of the whole sample using the 'Log-likelihood' checkbox.

You can also use the zoom buttons and arrows to adjust the views of the windows.

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