pkmon (version 1.1)

kKnot: k-Knot

Description

k-Knots of a discrete function.

Usage

kKnot(p, k)

Value

Vector with the k-knots of p.

Arguments

p

Vector

k

Degree of the knots

Author

Jade Giguelay

Details

An integer i is a k-knot of p if \(\Delta^k p(i) >0\), where \(\Delta^k\) is the k-th Laplacian of the sequence p.

References

Knopp K. (1925), <DOI:10.1007/BF01479598> Mehrfach monotone Zahlenfolgen, Mathematische Zeitschrift, 22, 75--85

Giguelay, J., (2016), Estimation of a discrete distribution under k-monotony constraint, in revision, (arXiv:1608.06541)

See Also

Delta

Examples

p=dmixSpline(c(5, 10, 20), k=3, c(0.5, 0.25, 0.25))
knots=kKnot(p, 3)