Order Statistics

The \(k\)-th order statistic of a sample is equal to its \(k\)-th smallest value. The \(k\)-th order statistic of a set of \(n\) values \(x = \left\{ x_i \right\}, 1 \le i \le n\) is denoted \(x_{(k)}\). The median of the set \(x\) is equal to \(x_{\left( \frac{n}{2} \right)}\) if \(n\) is odd, or the average of \(x_{\left( \frac{n}{2} \right)}\) and \(x_{\left( \frac{n}{2} + 1 \right)}\) if \(n\) is even. The \(k\)-th smallest element of a length \(n\) vector can be found in average \(O(n)\) time using the quickselect algorithm.

gsl_stats_select(data, f)

This function finds the k-th smallest element of the input array data.