histo {benchden} | R Documentation |
Name, position of modes, support and break points for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2010).
histo(dnum = 1)
dnum |
number of distribution. |
These functions implement the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2010). 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].
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. |
Thoralf Mildenberger
T. Mildenberger and H. Weinert, "The benchden Package: Benchmark Densities for Nonparametric Density Estimation", Journal of Statistical Software, vol. 46(14), 1-14, 2012. http://www.jstatsoft.org/v46/i14/
Y. Rozenholc, T. Mildenberger and U. Gather (2010), "Combining Regular and Irregular Histograms by Penalized Likelihood", Computational Statistics and Data Analysis, 54, 3313-3323. Earlier version including explicit definition of the densities: http://www.statistik.tu-dortmund.de/fileadmin/user_upload/SFB_823/discussion_papers/2009/31_09_rozenholc_mildenberger_gather.pdf
# 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