Freedman-Diaconis rule

From Wikipedia, the free encyclopedia

In statistics, the Freedman-Diaconis rule can be used to select the size of the bins to be used in a histogram. The general equation for the rule is:

$\mbox{Bin size}=2\, \mbox{IQR}(x) n^{-1/3} \;$

where

$\scriptstyle\operatorname{IQR}(x) \;$ is the interquartile range of the data

$\scriptstyle n \;$ is the number of observations in the sample $\scriptstyle x. \;$

[edit] Sturges' rule

Another approach is the use Sturges' rule: use a bin so large that there are about $\scriptstyle 1+\log_2n$ non-empty bins.

[edit] References

David Freedman and Persi Diaconis (1981). "On the histogram as a density estimator: L₂ theory." Probability Theory and Related Fields. 57(4): 453-476