Empirical Distributions

Empirical distribution is a very important estimator in Statistics. Many statistical procedures depend on its performances. In particular, the popular (nonparametric) Bootstrap method rely heavily on the empirical distribution.

To put it simply, the empirical distribution is a staircase function with the location of the drops randomly placed. Without censoring the size of the drops are always 1/n, with censoring the size of the drops also changes. Where n is the number of random observations this empirical distribution is based on. As n grows the empirical distribution will getting closer to the true distribution (plot in black, the one we used to generate the random observations). This also offers a visial check of how good the java's random number generator is.

This JAVA applet plots empirical distributions computed from a sample of iid exponential random variables. Starting with sample size n=2 and grew to as large as 10,000.

The true distribution, exponential, is ploted in black. Well, actually the survival function, 1-F(t), is plotted. So the black curve is just S(t)= exp(-t).

The empirical distribution is shown in red.


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Notes:

I welcome feedback and comments at mai@ms.uky.edu . Copyright 1998 Mai Zhou. All Rights Reserved.           back to my applet index page