On Saturday, October 20, 2012, Damon McDougall wrote:
> On Sat, Oct 20, 2012 at 10:25 PM, Steven Boada
> <bo...@physics.tamu.edu<javascript:;>>
> wrote:
> > It'd be cool if we could do something like
> >
> > bins = [(0.0,0.05,0.1),(0.05,0.1,0.15)...]
> >
> > Where I have specified the left edge, center and right edge of each
> > bin. Yeah, that'd be pretty slick.
> >
> > S
> >
> > On Sat Oct 20 16:21:41 2012, Steven Boada wrote:
> >> Let's say I generate a bunch of random numbers from 0-1. Then, I'd
> >> like to make a histogram of it. But here's the clincher. I'd like my
> >> bins to overlap a bit. For example, if the first bin is from 0 - 0.1,
> >> centered on 0.05, I'd like the next (second) bin to be centered on 0.1
> >> and range from 0.05 - 0.15.
> >>
> >> So basically, I want the width of each bin to be greater than the
> >> spacing.
> >>
> >> Is this something that could be done with the histogram function? I
> >> did a couple of google searches and couldn't come up with anything
> >> meaningful. Apparently, 'rwidth' in the hist function just makes the
> >> displayed bars bigger or smaller.
> >>
> >> Any thoughts?
> >>
> >
> > --
> >
> > Steven Boada
> >
> > Doctoral Student
> > Dept of Physics and Astronomy
> > Texas A&M University
> > bo...@physics.tamu.edu <javascript:;>
>
> My thoughts are that this goes against everything a histogram is set
> out to do; attempt to provide a 'discretised' probability distribution
> function given a set of discrete samples. Lets say a sample lies in
> the region where two bins overlap. How do you define which bin the
> sample lies in? Both? If both, how do you define the value of the
> approximated probability distribution on a bin? You could just take
> the height of the bin, but some of the bin's mass lies in each of the
> neighbouring bins.
>
> If you don't want to apply mass to the neighbouring bins for a sample
> that lies in the region where two bins overlap, you could just pick
> one. You then have the problem of non-uniqueness. If you'd picked the
> other bin you'd have a different probability distribution function.
> This a bad property to have.
>
> If you don't want to pick a neighbouring bin to apply more mass, and
> just increase the width of the each bin's matplotlib.patches.Patch
> object, then that is more sensible. Except now you have the problem of
> displaying the histogram. Which bin gets displayed over its left
> neighbour? And its right neighbour?
>
> I dread to think what this would imply if you also wanted to stack
> such histograms. A potential can of worms.
>
>
The closest I could think of as something reasonable is to apply a
convolution of some sort to the discrete pdf to produce an approximation of
a continuous PDF.
Cheers!
Ben Root
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