bberdev {benchden}

Some properties of 28 benchmark densities

Description

Names and points of nonsmoothness for the 28 distributions from Berlinet/Devroye (1994).

Usage

bberdev(dnum = 1)
nberdev(dnum = 1)

Arguments

dnum

number of distribution as in Berlinet/Devroye (1994), Section 3.2.

Details

These functions implement the 28 distributions from Berlinet and Devroye (1994), Section 3.2, which are:

dnum == 1 "uniform" on [0,1] as in stats-package

dnum == 2 "exponential" as in stats-package

dnum == 3 "Maxwell"

dnum == 4 "double exponential"

dnum == 5 "logistic" as in stats-package

dnum == 6 "Cauchy" as in stats-package

dnum == 7 "extreme value"

dnum == 8 "infinite peak"

dnum == 9 "Pareto"

dnum == 10 "symmetric Pareto"

dnum == 11 "normal" as in stats-package

dnum == 12 "lognormal"

dnum == 13 "uniform scale mixture"

dnum == 14 "Matterhorn"

dnum == 15 "logarithmic peak"

dnum == 16 "isosceles triangle"

dnum == 17 "beta 2,2" as in stats-package

dnum == 18 "chi-square 1" as in stats-package

dnum == 19 "normal cubed"

dnum == 20 "inverse exponential"

dnum == 21 "Marronite"

dnum == 22 "skewed bimodal"

dnum == 23 "claw"

dnum == 24 "smooth comb"

dnum == 25 "caliper"

dnum == 26 "trimodal uniform"

dnum == 27 "sawtooth"

dnum == 28 "bilogarithmic peak"

Value

nberdev

gives the name of the distribution (the same as name in berdev).

bberdev

Since evaluation of loss functions in nonparametric density estimation often requires numerical integration, bberdev returns a vector of points you should generally take care not to integrate over, e.g. points where the density is not continous or not differentiable (gives the same as breaks in berdev).

Author(s)

Thoralf Mildenberger, Henrike Weinert and Sebastian Tiemeyer

References

A. Berlinet and L. Devroye, "A comparison of kernel density estimates", Publications de l'Institut de Statistique de l'Universite de Paris, vol. 38(3), pp. 3-59, 1994. https://hal.science/hal-03659919

T. Mildenberger and H. Weinert, "The benchden Package: Benchmark Densities for Nonparametric Density Estimation", Journal of Statistical Software, vol. 46(14), 1-14, 2012. https://www.jstatsoft.org/v46/i14/

Examples

# name of "Claw"-distribution
nberdev(dnum=23)