Introduction The cross validation is a common technique to calibrate the binwidth histogram. They are the simplest and, sometimes, the most effective tool to describe the density of some dataset.

Two popular methods to find the bandwidth $latex {h}&fg=000000$ for the nonparametric density estimator are the plug-in method and the method cross-validation. The first one we will focus in the “quick and dirty” plug-in method introduced by Silverman (1986). In cross-validation we will minimize a modified version of the quadratic risk of $latex {\hat{f}_{h}}&fg=000000$. The …