Understanding order statistics

Order statistics are the values of a collection of samples when arranged in ascending or descending order. These ordered samples provide useful information about the distribution and characteristics of the sampled data. Usually, the k th order statistic is the k th smallest value in the sorted sample.

For example, for a collection of samples of size n, the order statistics are denoted as X 1, X 2, … , X n, where X 1 is the smallest value (the minimum), X n is the largest value (the maximum), and X k represents the k th smallest value in the sorted sample.

Let’s look at how to extract order statistics in R.

Extracting order statistics

Extracting the order statistics of a collection of samples could involve two types of tasks. We may be interested in collecting samples in an ordered fashion, which can be achieved using the sort() function. Alternatively, we may be interested in extracting...