bhisto {benchden}R Documentation

Some properties of 4 histogram benchmark densities

Description

Names and breakpoints for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2009).

Usage

bhisto(dnum = 1)
nhisto(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

nhisto gives the name of the distribution (the same as name in histo).
bhisto gives the vector of break points (the same as breaks in histo).

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


# name string of 5 bin regular histogram
nhisto(dnum=1)


[Package benchden version 1.0.3 Index]