dhisto {benchden} | R Documentation |
Density, distribution function, quantile function and random variate generation for the 4 histogram benchmark distributions from Rozenholc/Mildenberger/Gather (2010).
dhisto(x,dnum = 1) phisto(q,dnum = 1) qhisto(p,dnum = 1) rhisto(n,dnum = 1)
dnum |
number of distribution as in Rozenholc/Mildenberger/Gather (2010) |
x,q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
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].
dhisto |
gives the density, |
phisto |
gives the distribution function, |
qhisto |
gives the quantile function, and |
rhisto |
generates random deviates. |
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
# 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"))