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| Science Forum Index » Statistics - Math Forum » (Apparent) Non-convergence of uniform data.... |
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| Bacle... |
 Posted: Tue Nov 03, 2009 6:20 pm |
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Hi, everyone:
I am working with a software package that generates
random data of different sizes from both a normal
population and a uniform population. The data
generated is then plotted (histograms.)
What I am curious about is a noticeable difference
between the histograms of the samples from a normal population vs. the histograms of samples from a uniform population:
With the normal population, as the data size grows, the histograms very quickly start looking like the parent distribution, i.e., the histograms do look normally-distributed, even for samples of size n=100.
For the uniform population, though, the histograms do not approach (in a purely visual sense) a uniform distribution, even for samples of sizes 1,000 or 10,000.
Can anyone suggest what is happenning, i.e., why the histograms of the uniform data points do not approach a uniform plot.?
Thanks For any Help. |
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| Bacle... |
| Posted: Tue Nov 03, 2009 6:29 pm |
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Guest
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Sorry: after taking larger and larger samples, I did
note the (purely visual) convergence of the histograms
to a uniform distribution.
An issue that remains, though, is that the convergence
to a normal distribution seems much faster than that of the uniform distribution.
Is this difference in convergence rates just an accident, or am I missing something, some result that
would warrant this different rate of convergence.?
Thanks. |
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| Ray Koopman... |
| Posted: Tue Nov 03, 2009 7:56 pm |
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On Nov 3, 8:29 pm, Bacle <ba... at (no spam) yahoo.com> wrote:
[quote]Sorry: after taking larger and larger samples, I did
note the (purely visual) convergence of the histograms
to a uniform distribution.
An issue that remains, though, is that the convergence
to a normal distribution seems much faster than that of the uniform distribution.
Is this difference in convergence rates just an accident, or am I missing something, some result that
would warrant this different rate of convergence.?
Thanks.
[/quote]
It may be a purely visual-perceptual problem. Instead of plotting the
observed count in each bin, try plotting the difference between the
observed and expected counts in each bin. Then a "perfect" sample will
give a flat line, no matter what population you're sampling from. |
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| David Jones... |
| Posted: Wed Nov 04, 2009 6:29 am |
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Ray Koopman wrote:
[quote]On Nov 3, 8:29 pm, Bacle <ba... at (no spam) yahoo.com> wrote:
Sorry: after taking larger and larger samples, I did
note the (purely visual) convergence of the histograms
to a uniform distribution.
An issue that remains, though, is that the convergence
to a normal distribution seems much faster than that of the uniform
distribution.
Is this difference in convergence rates just an accident, or am I
missing something, some result that would warrant this different
rate of convergence.?
Thanks.
It may be a purely visual-perceptual problem. Instead of plotting the
observed count in each bin, try plotting the difference between the
observed and expected counts in each bin. Then a "perfect" sample will
give a flat line, no matter what population you're sampling from.
[/quote]
This might not solve the visual-perceptual problem: an improved version is the hanging rootogram ... see for example http://www.math.yorku.ca/SCS/Gallery/bright-ideas.html . But, for comparisons between distributions, where there are large differences in the expected numbers in each cell it might be better to use a different scaling, perhaps most simply by plotting the signed-square root of the cell's contribution to a chi-squared test.
David Jones |
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| Gordon Sande... |
| Posted: Wed Nov 04, 2009 8:39 am |
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On 2009-11-03 19:29:36 -0400, Bacle <bacle at (no spam) yahoo.com> said:
[quote]Sorry: after taking larger and larger samples, I did
note the (purely visual) convergence of the histograms
to a uniform distribution.
An issue that remains, though, is that the convergence
to a normal distribution seems much faster than that of the uniform
distribution.
Is this difference in convergence rates just an accident, or am I
missing something, some result that
would warrant this different rate of convergence.?
Thanks.
[/quote]
How many bins for how many observations? If the number of observations per bin
remains the same this is to be expected although it is not quite what one would
expect from a typical graphing program.
Nor everyones notion of "visual convergence" will be the same so the question
has many answers beyond the merely technical.  |
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