Sturges’ and Scott’s Rules

Introduction

The fundamental object of modern statistics is the random variable X and its associated probability law. The probability law may be given by the cumulative probability distribution F(x), or equivalently by the probability density function f(x) = F′(x), assuming the continuous case. In practice, estimation of the probability density may approached either parametrically or nonparametrically. If a parametric model f(x | θ) is assumed, then the unknown parameter θ may be estimated from a random sample using maximum likelihood methods, for example. If no parametric model is available, then a nonparametric estimator such as the histogram may be chosen. This article describes two different methods of specifying the construction of a histogram from a random sample.

Histogram as Density Estimator

The histogram is a convenient graphical object for representing the shape of an unknown density function. We begin by reviewing the stem-and-leaf diagram, introduced by Tukey (1977)....