benchden (version 1.0.8)

berdev: Some Properties of 28 benchmark densities

Description

Name, position of modes, support and points of nonsmoothness for the 28 distributions from Berlinet/Devroye (1994).

Usage

berdev(dnum = 1)

Value

berdev returns a list with components

name

gives the name of the distribution,

peaks

gives a vector of the positions of peaks or modes of the density, and

support

gives a matrix as follows: in each row an interval is defined (with the first column giving the left and the second column the right end of the interval). Together the intervals give the support of the distribution (for most distributions only one interval).

breaks

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.

Arguments

dnum

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

Author

Thoralf Mildenberger, Henrike Weinert and Sebastian Tiemeyer

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"

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

# position of peaks of "Claw"-distribution
berdev(dnum=23)$peaks

# support of the "Trimodal uniform"
berdev(dnum=26)$support