histo {benchden}R Documentation

Some properties of 4 histogram benchmark densities

Description

Name, position of modes, support and break points for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2009).

Usage

histo(dnum = 1)

Arguments

dnum number of distribution.

Details

These functions implement the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2009). Defined as the following mixtures of uniform distributions:

dnum == 1 5 bin regular histogram:

0.15*U[0,0.2] + 0.35*U(0.2,0.4] + 0.2*U(0.4,0.6] +0.1*U(0.6,0.8]+ 0.2*U(0.8,1.0]

dnum == 2 5 bin irregular histogram:

0.15*U[0,0.13] + 0,35*U(0.13,0.34] + 0.2*U(0.34,0.61] +0.1*U(0.61,0.65] + 0.2*U(0.65,1.0]

dnum == 3 10 bin regular histogram:

0.01*U[0,0.1] + 0.18*U(0.1,0.2] + 0.16*U(0.2,0.3]

+0.07*U(0.3,0.4] + 0.06*U(0.4,0.5] + 0.01*U(0.5,0.6]

+0.06*U(0.6,0.7] + 0.37*U(0.7,0.8] + 0.06*U(0.8,0.9]

+0.02*U(0.9,1.0]

dnum == 4 10 bin irregular histogram:

0.01*U[0,0.02] + 0.18*U(0.02,0.07] + 0.16*U(0.07,0.14]

+0.07*U(0.14,0.44] + 0.06*U(0.44,0.53] + 0.01*U(0.53,0.56]

+0.06*U(0.56,0.67] + 0.37*U(0.67,0.77] + 0.06*U(0.77,0.91]

+0.02*U(0.91,1.0]

where U[a,b] denotes the uniform distribution on [a,b].

Value

histo returns a list with the following components:

name gives the name of the distribution.
peaks gives a vector of the positions of peaks of the density, defined here as mid points of maximal intervals.
support gives a matrix with one row with the endpoints of the support, which is [0,1] for all four histogram densities.
breaks gives the vector of break points.

Author(s)

Thoralf Mildenberger

References

Y. Rozenholc, T. Mildenberger and U. Gather, "Combining Regular and Irregular Histograms by Penalized Likelihood", Discussion Paper 31/2009, SFB 823, TU Dortmund. http://www.statistik.tu-dortmund.de/fileadmin/user_upload/SFB_823/discussion_papers/2009/31_09_rozenholc_mildenberger_gather.pdf

Examples


# position of peaks of the 5 bin irregular histogram density
histo(dnum=2)$peaks

# support of the 10 bin regular histogram density
histo(dnum=3)$support


[Package benchden version 1.0.3 Index]