INTERACTIVE ANIMATION: ORDER STATISTICS OF THE UNIFORM DISTRIBUTION

The following interactive animation illustrates the concept of order statistics in the special case of the uniform distribution.

Upper frame

    The upper frame displays:

        * The [0, 1] segment, sandwiched between two green "walls".

        * A sample drawn from the uniform distribution in [0, 1].

The sample has n observations, with n as indicated ins the "Sample size" display. Use the "Sample size" spin buttons to change the number of observations in the sample.

Observations are blue, except for the k^th observation from the left, which is red. The value of k is indicated in the "Rank" display. Change the value of k with the "Rank" spin buttons.

Lower frame

    The lower frame displays:

        * The probability density function of the k^th order statistics of the uniform distribution.

        * The abscissa of the (unique) mode.

        * The height of this mode.

Observe the changes in the shape of the curve as you change the number of observations and the requested order.

    * In general, the curve is bell-shaped, and materializes a Beta function. As a matter of fact, order statistics of uniform distributions have Beta distributions.

    * Extreme observations (Leftmost and Rightmost) have monotonous distributions. For example, the closer to 0, the better are the chances to locate the leftmost observation.

    * When there are only 2 observations, both observations have linear pdf s.

Animation

    Select a number of observations and a rank. Then click on "Go" and observe the build up of the histogram of the corresponding order statistics.