Re: Number of bins in a histogram

In article <1147996185.826078.78460@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Reef Fish <Dr_Bob_Ling@xxxxxxxxx> wrote:

Herman Rubin wrote:
In article <1147973306.100992.295490@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Lou Thraki <louthraki@xxxxxxxxx> wrote:
Can someone give, or refere to, an explanation where the
1/N^(1/3) in the Freedman-Diakonis rule for the number of
bins in a histogram comes from?

There are two sources of error in estimating a
density from a histogram. One is the coarseness
of the histogram, and the other is the inaccuracy
of the height of a bin. For the first, lots of
bins are better, and for the second, large bins
are better. These two errors balance at the
order of magnitude quoted.

A histogram has been said to be the WORST possible tool
to use for the assessment of continuous distributions.

I definitely agree. However, I was answering the question.

A histogram concentrates on the CENTER of a distribution.
while the TAIL of a distribution is most distinct part of it,
in distinguishing it from a Normal Distrbution, say.

This is some of the fault of essentially all of the
procedures. Kernel estimates are overly poor in the
tails, unless the kernel gets wider, and the effect
is greater for the larger tailed distributions.
Nearest neighbor procedures CAN produce estimates
with finite integral, but not the crude ones in use.

At this time, I know of no way of estimating densities
which is not ad hoc with lots of hidden assumptions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

Relevant Pages

  • Re: Number of bins in a histogram
    ... density from a histogram. ... bins are better, and for the second, large bins ... to use for the assessment of continuous distributions. ... as well as non-parametric density estimation methods. ...
    (sci.stat.math)
  • Re: The Promise of Forth
    ... Returns the computed median value of a list of numbers, ... number of bins to use for the histogram (more bins brings the computed value ... Association for Computing Machinery Inc., New York, ...
    (comp.lang.forth)
  • Re: Histogram equalization
    ... There is nothing in MATLAB that does accurate histogram matching. ... transform it accurately to the histogram of the second image. ... certain bins with other bins completely empty. ... get a very flat histogram and ALL the bins will be filled up. ...
    (comp.soft-sys.matlab)
  • Problem overlaying data on .gif
    ... I'm plotting some satellite data (latitude, ... every time step) in a 2d histogram (using hist2d from mathworks) so I ... % spaced bins in both dimensions ...
    (comp.soft-sys.matlab)
  • Re: Histogram and Normality test
    ... but the data always fails the normality ... When plotting the histogram with 1000 bins, ... various spikes in the figure. ...
    (comp.soft-sys.matlab)