pkmon (version 1.1)

BaseNorm: Normalized spline basis

Description

Computes the k-monotone discrete splines from Lefevre and Loisel (2013).

Usage

BaseNorm(k, J)

Value

matrix \(Q\) with J+1 rows and J+1 columns with \(Q(i,j)=Q_j^k(i-1)=C_{j-i+k-1}^{k-1}\), where \(C\) represents the binomial coefficient.

Arguments

k

Degree of monotony

J

maximum support of the splines

Author

Jade Giguelay

References

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

Lefevre C., Loisel S. (2013) <DOI:10.1239/jap/1378401239> On multiply monotone distributions, continuous or discrete, with applications, Journal of Applied Probability, 50, 827--847.

See Also

rSpline, dSpline, rmixSpline, dmixSpline

Examples

# Computing 3-monotone splines with maximum support 8
Q=BaseNorm(3, 8)
matplot(Q, type="l", main="3-monotone splines with maximum support 8");