pkmon (version 1.1)

Spline: Random generation and distribution function of k-monotone densities

Description

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

Usage

rSpline(n=1, supp, k)
dSpline(supp, k)
rmixSpline(n=1, supp, k,prob)
dmixSpline(supp, k, prob)

Value

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

dSpline and dmixSpline gives the distribution function.

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

Author

Jade Giguelay

Details

See BaseNorm for details on the spline basis.

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

pEmp

Examples

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")