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Biometrika 1979 66(3):605-610; doi:10.1093/biomet/66.3.605
© 1979 by Biometrika Trust
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On optimal and data-based histograms

DAVID W. SCOTT

Department of Mathematical Sciences, Rice University Houston, Texas

In this paper the formula for the optimal histogram bin width is derived which asymptotically minimizes the integrated mean squared error. Monte Carlo methods are used to verify the usefulness of this formula for small samples. A data-based procedure for choosing the bin width parameter is proposed, which assumes a Gaussian reference standard and requires only the sample size and an estimate of the standard deviation. The sensitivity of the procedure is investigated using several probability models which violate the Gaussian assumption.

Key Words: Frequency distribution • Histogram • Nonparametrio density estimation • Optimal bin width


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