Histogram: Difference between revisions

Revision as of 21:06, 21 April 2013

Revision as of 01:16, 22 April 2013

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:<math> \sigma_{g_1} = \sqrt { \frac { 6(n-2) }{ (n+1)(n+3) } } </math>

;Scott's normal reference rule:

;Scott's normal reference rule:<ref name=scott79>{{cite journal |last=Scott |first=David W. |year=1979 |title=On optimal and data-based histograms |journal=Biometrika |volume=66 |issue=3 |pages=605–610 |doi=10.1093/biomet/66.3.605 }}</ref>

:<math>h = \frac{3.5 \hat \sigma}{n^{1/3}},</math>

where <math>\hat \sigma</math> is the sample [[standard deviation]]. Scott's normal reference rule<ref name=scott79>{{cite journal |last=Scott |first=David W. |year=1979 |title=On optimal and data-based histograms |journal=Biometrika |volume=66 |issue=3|pages=605–610 |doi=10.1093/biomet/66.3.605}}</ref> is optimal for random samples of normally distributed data, in the sense that it minimizes the integrated mean squared error of the density estimate.<ref name=scott92>{{cite book|last=Scott|first=D.|middle=David W.|title=Multivariate Density Estimation: Theory, Practice, and Visualization|publisher=John Wiley|___location=New York|year=1992|ref=harv}}</ref>

;Freedman–Diaconis' choice

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which is based on the [[interquartile range]], denoted by IQR. It replaces 3.5σ of Scott's rule with 2 IQR, which is less sensitive than the standard deviation to outliers in data.

; Choice based on minimization of an estimated ''L''² [[risk function]]:<ref>{{cite journal | last = Shimazaki | first =H. | authorlink = | coauthors =Shinomoto, S. | title =A method for selecting the bin size of a time histogram | journal = Neural Computation | volume =19 | issue = 6 | pages =1503–1527 | publisher = | year =2007 | url = http://www.mitpressjournals.org/doi/abs/10.1162/neco.2007.19.6.1503 | pmid = 17444758 | doi = 10.1162/neco.2007.19.6.1503 }}</ref> [[risk function]]:

:<math> \underset{h}{\operatorname{arg\,min}} \frac{ 2 \bar{m} - v } {h^2} </math>