Distributions of Order Statistics

sample size

4

density function

tent density

uniform density

hump on the left

hump on the right

If

n

independent values are drawn from some distribution and ordered from smallest to largest, the

th

r

value is the

th

r

order statistic. The distribution of this value depends on both the underlying distribution and the size of the sample,

n

. In this Demonstration, you can choose among four probability distributions on the unit interval and view the distributions of the order statistics for that distribution for samples of various sizes. Mouse over the curves to view the means of the various distributions in the image.