# What does this simple notation mean?

1. Jun 4, 2009

### hassman

$$X_{n:n}$$

where X is a random variable. Searched the internots but couldnt find anything

2. Jun 4, 2009

### statdad

Some authors use this to denote the largest order statistic in a sample of size n - in notation

$$X_{n:n} = X_{(n)}$$

is the largest order statistic.

You will also occasionally see this notation used in connections of double arrays of random variables, usually when a type of limit theorem is being discussed. (double array = arrangement of rows, with number of entries increasing with each row, to illustrate growing sample sizes)

There may be others.
In what context did you encounter this?

3. Jun 4, 2009

### hassman

Thanks a lot. I was using search term "rank statistic" instead of "order statistic".

This is in the context of largest insurance claim.

4. Jun 4, 2009

### statdad

A "rank statistic" is a statistic calculated based on the ranks of the data. The smallest data value has rank 1, the next smallest rank 2, and so on. Much of the calculation and theory (to determine distributions) of rank statistics can be expressed in terms of the order statistics.

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