FreedmanDiaconis

Freedman–Diaconis is a statistical guideline for choosing the bin width in histograms. Named after mathematician David Freedman and statistician Persi Diaconis, the rule was introduced in a 1981 paper on histogram density estimation and robust data analysis. It aims to provide a practical balance between bias and variance in the histogram representation of data.

The rule specifies the bin width h as h = 2 × IQR / n^(1/3), where IQR is the interquartile range (the difference between the 75th and 25th percentiles) and n is the sample size. The approximate number of bins is then determined by dividing the data range by h. This makes the method responsive to the data’s spread while remaining robust to outliers, since IQR is a robust measure of dispersion.

Compared with other common rules, the Freedman–Diaconis rule is more robust to outliers than Scott’s rule, which uses the standard deviation, and it is often more data-adaptive than Sturges’ rule, which tends to under-bin large datasets. It is widely used in exploratory data analysis and data visualization in statistics and data science.

Limitations include sensitivity to the accuracy of the IQR estimate in very small samples and potential over- or under-smoothing for multimodal distributions. Nevertheless, for many practical datasets, the Freedman–Diaconis rule provides a robust, simple default for histogram binning.