BIN-WIDTH CORRECTION OF HISTOGRAM IN A FINITE INTERVAL

Abstract

We consider Histograms in a finite interval. Constructing Histograms requires an anchor position and a bin width which correspond to parameters. The Histogram generally cannot be estimated to match a finite interval, in situations where the anchor position is determined at the leftmost of the finite interval and the bin width is estimated from the data. We have a simple idea to eliminate the gap called the "bin residuals". It is to divide the bin residual evenly into each bins and correct the bin width. In this paper, we show the asymptotic properties of this correction. To clarify its usefulness, we also examine characteristics in finite samples by numerical experiments. Since it is a simple correction method, it can be applied various bin-width estimation methods.