HistOptimal: Matlab toolbox available on the Mathworks File Exchange named, realized for Birgé, Rozenholc (2006), uses regular histograms only.

PenPolExp: Matlab toolbox developed with E. BRAMI and H. THABET. This toolbox does the estimation of the unknown density using piecewise exponential of polynoms where the number of pieces and the degree of the polynom on each piece is automatically selected. This toolbox implements ideas of Castellan (2003) -.

> X = randn(1000,1)

> H = HistOptimal(X)

Histogram: R-package available on the CRAN, realized for Rozenholc, Mildenberger and Gather (2009), uses regular and/or irregular histograms.

> library(histogram)

> X = rnorm(1000)

> histogram(X)

> X = (0.5+rexp(1000))*sign(rnorm(1000))

> histogram(X)

> histogram(X,type=‘regular’)          # force regular

> histogram(X,type=‘irregular’)        # force irregular

> X = rnorm(1000)

> [Beta,Bounds]=PenExpDens(X);

> PlotPiecewiseExpPoly(Beta,Bounds);

>

> X = [randn(700,1);4+randn(300,1)];

> [Beta,Bounds]=PenExpDens(X);

> PlotPiecewiseExpPoly(Beta,Bounds);

Keywords: density estimation, histogram, model selection, penalized maximum likelihood estimator, piecewise polynomial, exponential model