# The Kaplan-Meier Estimator

The Kaplan-Meier's 1958 paper is one of the top 5 most referenced papers in the field of Sciences --- An indication of its importance.

To put it simply, the Kaplan-Meier estimator is a staircase function with (1) the location of the drops randomly placed (at the observed failure times). (2) due to censoring, the size of the drops also changes (increase as time increase or as censoring counts increases).

This JAVA applet plots the Kaplan-Meier estimator computed from a sample of iid exponential random variables. The censoring times are also iid exponential random variables-- thus for each observation there is 50% chance been censored (adjustable). Starting with sample size n=2 and grew to as large as sample size 10,000.

In the new version there is choice of several censoring percentage.

As n grows the Kaplan-Meier estimator will getting closer to the true distribution (plotted in black, the one we used to generate the random observations).

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

The Kaplan-Meier estimator is shown in red. Following conventional plotting, I have put a little tick on the censored observations. For large samples this just makes the red curve 4 pixels wide.

Notes:

• The y axis is drawn at 0, the curve starts at 1 and drops down to zero. I am too lazy to put units on the axis. Every time n increases the computation pauses for half a second. (for those want speed instead of detail, I may put up a button for speed adjustment in the future). Also if n exceeds 10000 the computation will be messed up since I have limited the storage to 10000. But after n exceed, say, 3000, the red curve do not change much and almost coincide with the black curve. This is still under improvement.... change of censoring percentage is added Oct. 1998).
• Runs under Netscape 3.0 and up. Not (yet) tested under other browser.
• A picture of Paul Meier taken in 2006 by me.  back to my applet index page