dhisto {benchden}R Documentation

4 histogram benchmark densities

Description

Density, distribution function, quantile function and random variate generation for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2009).

Usage

dhisto(x,dnum = 1)
phisto(q,dnum = 1)
qhisto(p,dnum = 1)
rhisto(n,dnum = 1)

Arguments

dnum number of distribution as in Rozenholc/Mildenberger/Gather (2009)
x,q vector of quantiles.
p vector of probabilities.
n number of observations.

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

dhisto gives the density,
phisto gives the distribution function,
qhisto gives the quantile function, and
rhisto generates random deviates.

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


# histogram and true density of "5 bin irregular"-distribution
hist(rhisto(2000,dnum=2),breaks=250, main = " ",freq=FALSE)
lines(seq(0,1,0.01),dhisto(seq(0,1,0.01),dnum=2),col="blue",lwd=1)
title(paste("sample from",nhisto(dnum=2),"density"))


[Package benchden version 1.0.3 Index]