# Spline: Random generation and distribution function of k-monotone... In pkmon: Least-Squares Estimator under k-Monotony Constraint for Discrete Functions

## Description

Random generation and distribution function for the spline of the basis from Lefevre and Loisel (2013), and mixtures of splines.

## Usage

 ```1 2 3 4``` ```rSpline(n=1, supp, k) dSpline(supp, k) rmixSpline(n=1, supp, k,prob) dmixSpline(supp, k, prob) ```

## Arguments

 `supp` Support of the spline, or vector of the supports of the splines for the mixture of splines `n` Number of random values to return `k` Degree of monotony `prob` Vector of probabilities for the mixture of splines

## Details

See BaseNorm for details on the spline basis.

## Value

rSpline and rmixSpline generates random deviates from the splines and mixtures of splines.

dSpline and dmixSpline gives the distribution function.

## 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.

 ```1 2 3 4 5 6 7 8 9``` ```x=rSpline(n=100, 20, 3) p=dSpline(20, 3) xmix=rmixSpline(n=100, c(5, 20), 3, c(0.5, 0.5)) pmix=dmixSpline(c(5, 20), 3, c(0.5, 0.5)) par(mfrow=c(1, 2)) hist(x, freq=FALSE) lines(p, col="red") hist(xmix, freq=FALSE) lines(pmix, col="red") ```