Interval censored data of type 1 is also called current status data or binary data. In this case the variable of interest, X, is never observed exactly. We only observe Y and if (X>Y) or not. (The status of X at current time Y).

The Non-parametric Maximum Likelihood Estimator (NPMLE) of distribution of X is a staircase function with the location of the drops randomly placed. The size of the drops also changes.

This JAVA applet plots NPMLE of distributions computed from a sample of current status data. We took both X and Y to be standard exponential random variables. Starting with sample size n=2 and grew to as large as 10,000.

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

The NPMLE is shown in red.

The NPMLE converge very slowly, in fact, it is known to converge at a rate of 1/cubic root(n). As opposed to the Kaplan-Meier estimator which converge at a rate of 1/square root(n).

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 a while (0.2 second). The speed adjustment doubles or halfs the pause time. Also if n exceeds 10000 the computation will be messed up since I have limited the storage to 10000. This is still under improvement.....
• Runs under Netscape 3.01 and up. Not (yet) tested under other browser. Many thanks to Kun Chen for help me with the java code.

I welcome feedback and comments at mai@ms.uky.edu . Copyright © 1998 Mai Zhou. All Rights Reserved.