orderstats: Compute Order Statistics

In spatstat/spatstat.utils: Utility Functions for 'spatstat'

Compute Order Statistics

Description

Compute the k-th smallest value in a dataset, or find which entry in a dataset is the k-th smallest.

Usage

orderstats(x, k, decreasing = FALSE)
orderwhich(x, k, decreasing = FALSE)

Arguments

x	Data whose order statistics will be computed. A numeric vector.
k	Rank. An integer, or vector of integers.
decreasing	Logical value specifing whether a rank of 1 is assigned to the highest value (decreasing=TRUE) or the lowest value (decreasing=FALSE, the default).

Details

These are low-level functions for efficiently computing order statistics: orderstats(x, k) returns the k-th smallest value in x, and orderwhich(x, k) returns the position of the k-th smallest value in x.

Given a dataset of values x_1, \dots, x_n, the order statistic of rank k is the k-th smallest value in the dataset. The order statistic of rank 1 is the smallest value, and the order statistic of rank n is the largest value. The order statistic of rank k is denoted x_{[k]}.

The full sequence of order statistics

x_{[1]} \le x_{[2]} \le \dots \le x_{[n]}

can simply be obtained by sorting the original values into increasing order.

The command orderstats(x, k) is equivalent to sort(x)[k]; it calculates the k-th smallest value in x.

The command orderwhich(x, k) is equivalent to order(x)[k]. It identifies the position of the k-th smallest value in x, that is, it returns the index j such that x[j] is the k-th smallest value in x.

The functions orderstats and orderwhich are more efficient than using sort and order when it is only desired to calculate a few of the order statistics (for example, only the smallest and second-smallest values in the dataset).

Value

orderstats returns a vector of the same kind as x, with the same length as k. orderwhich returns an integer vector with the same length as k.

Author(s)

\adrian

.

See Also

sort, order.

Examples

  x <- runif(10)
  orderstats(x, 2)
  sort(x)[2]
  orderwhich(x, 2:3)
  order(x)[2:3]

spatstat/spatstat.utils documentation built on Oct. 25, 2023, 10:07 p.m.