Simple and effective number-of-bins circumference selectors for a histogram

Two very effective data-based procedures which are simple and fast to compute are proposed for selecting the number of bins in a histogram. The idea is to choose the number of bins that minimizes the circumference (or a bootstrap estimate of the expected circumference) of the frequency histogram. Contrary to most rules derived in the literature, our method is therefore not dependent on precise asymptotic analyses. It is shown by means of an extensive Monte-Carlo study that our selectors perform well in comparison with recently suggested selectors in the literature, for a wide range of density functions and sample sizes. The behaviour of one of the proposed rules is also illustrated on real data sets.