Names and breakpoints for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2010).
bhisto(dnum = 1)
nhisto(dnum = 1)gives the name of the distribution (the same as name in histo).
gives the vector of break points (the same as breaks in histo).
number of distribution.
Thoralf Mildenberger
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 \([a,b]\).
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/
Y. Rozenholc, T. Mildenberger and U. Gather (2010), "Combining Regular and Irregular Histograms by Penalized Likelihood", Computational Statistics and Data Analysis, 54, 3313-3323. tools:::Rd_expr_doi("10.1016/j.csda.2010.04.021") Earlier version including explicit definition of the densities: tools:::Rd_expr_doi("10.17877/DE290R-15901")
# name string of 5 bin regular histogram
nhisto(dnum=1)
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