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.?
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.?
> 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.
Ray Koopman wrote: > On Nov 3, 8:29 pm, Bacle <ba...@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.
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.
On 2009-11-03 19:29:36 -0400, Bacle <ba...@yahoo.com> said:
> 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.
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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