ESTIMATION OF THE CENTER OF A SYMMETRIC DISTRIBUTION
This applet illustrates several competing estimators for the center
of a symmetric distribution. The user is allowed to select the
sample size, parent distribution, and number of replications for
sampling.
The demonstration generates a specified number samples of
specified size when the Run button is pressed (or a distribution
is double clicked in the list). For each
sample, all of the competing estimators of the center are
calculated. Once all samples are generated and all
estimators calculated, several summary views may be
illustrated.
There are two sets of radio buttons for the estimators. The left
column indicates the presence of the associated estimator in the
kernel density estimates plot and the boxplots. You may select
as many or as few of the estimators as you wish for these illustrations,
and all are included by default.
The right set of radio buttons allows only one estimator to be selected
at a time. This selection is illustrated when the histogram and
statistics buttons are used.
As you use the applet, note that the best estimator is different for
different generating populations.
The T(.1,3) N(0,1) is the Tukey model of a mixture of
two normal distributions: 90% of a Normal(0,1) and 10% of a Normal(0,9).
Note that the estimators are color coded to make them easy to find
in the plots. Also note that when you choose large sample sizes and
a large number of replications, the estimation may take a little while
due largely to the two maximum likelihood estimators. These estimators
are calculated using Newton-Raphson (optimizing stepsize).
Click the Run button below when the applet has completed loading.