“Freedman–Diaconis rule”的意思、由来-开放百科全书

In statistics, the Freedman–Diaconis rule can be used to select the width of the bins to be used in a histogram.^[1] It is named after David A. Freedman and Persi Diaconis.

For a set of empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed to minimize the difference between the area under the empirical probability distribution and the area under the theoretical probability distribution.{{Clarify|reason=What is the empirical probability distribution? Why would minimizing this difference be a good thing?|date=June 2017}}

where

is the interquartile range of the data and

is the number of observations in the sample

Other approaches

Another approach is to use Sturges' rule: use a bin so large that there are about

non-empty bins (Scott, 2009).^[2] This works well for n under 200, but was found to be inaccurate for large n.^[3]

References

1. ^{{cite journal|last=Freedman|first=David|last2=Diaconis|first2=Persi|date=December 1981|title=On the histogram as a density estimator: L₂ theory|journal=Probability Theory and Related Fields|volume=57|issue=4|pages=453–476|doi=10.1007/BF01025868|issn=0178-8051|authorlink=David Freedman (statistician)|authorlink2=Persi Diaconis|citeseerx=10.1.1.650.2473}}
2. ^{{Cite journal | last1 = Scott | first1 = D.W. | year = 2009 | title = Sturges' rule | url = | journal = WIREs Computational Statistics | volume = 1 | issue = 3| pages = 303–306 | doi=10.1002/wics.35}}
3. ^{{Cite journal | last1 = Hyndman | first1 = R.J. | year = 1995 | title = The problem with Sturges' rule for constructing histograms | url = http://robjhyndman.com/papers/sturges.pdf | journal = | volume = | issue = | pages = | doi= }}
4. ^{{Cite journal | last1 = Birgé | first1 = L. | last2 = Rozenholc | first2 = Y. | year = 2006 | title = How many bins should be put in a regular histogram | url = http://www.numdam.org/item?id=PS_2006__10__24_0 | journal = ESAIM: Probability and Statistics | volume = 10 | issue = | pages = 24–45 | doi=10.1051/ps:2006001| citeseerx = 10.1.1.3.220 }}