kthPair: K-th largest element in a sum of sets.

In robcp: Robust Change-Point Tests

K-th largest element in a sum of sets.

Description

Selects the k-th largest element of X + Y, a sum of sets. X + Y denotes the set \{x + y | x \in X, y \in Y\}.

Usage

kthPair(X, Y, k, k2 = NA)

Arguments

X	Numeric vector.
Y	Numeric vector.
k	Index of element to be selected. Must be an integer and between 1 and the product of the lengths of x and y.
k2	Optional second index. k and k2 must be consecutive. Useful, if the number of elements of X + Y is even and the median is to be calculated.

Details

A generalized version of the algorithm of Johnson and Mizoguchi (1978), where X and Y are allowed to be of different lengths. The optional argument k2 allows the computation of the mean of two consecutive value without running the algorithm twice.

Value

K-th largest value (numeric).

Author(s)

Sheila Görz

References

Johnson, D. B., & Mizoguchi, T. (1978). Selecting the K-th Element in X+Y and X_1+X_2+ ... +X_m. SIAM Journal on Computing, 7(2), 147-153.

Examples

set.seed(1895)
x <- rnorm(100)
y <- runif(100)

kthPair(x, y, 5000)
kthPair(x, y, 5000, 5001)

robcp documentation built on April 11, 2025, 6:18 p.m.