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Science Forum Index » Math - Numerical Analysis Forum » Bell shaped curves
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| Stig Holmquist |
 Posted: Tue Jan 09, 2007 12:03 pm |
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The most common bell shaped curve is the normal or Gaussian but
not all data forming a symmetrical bell shaped curve are normal.
I wen to Google to search for other bell curves but found none.
Is there a book discussing other bell curves and how to find
their standard deviation from the mean? E.g the frequencies
for the popular lotto game Powerball is based on take 5
out of 55 and can yield about 3.5 million combinations.
The sums of the various stets of five numbers can range
from 15 to 265 and their frequencies have a peak value
of 39361 at 140 but a plot of all frequencies do not fit a
normal curve perfectly. If the curve were perfectly normal
one could calculate the std.dev. from the mean 140 by
mutiplying the total by 0.4 and dividing by 39361 but this
yields a value of 33.63 after 142 draws, which is less than
the " theoretical" value of 35.4. The cumulative s.d
seems to approach 33.5.
Without actually calculating the s.d. for the total set
of 3.5 million how might one estimate most accurately
the s.d. for the toatal set?
Stig Holmquist |
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| Han de Bruijn |
| Posted: Wed Jan 10, 2007 3:53 am |
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Stig Holmquist wrote:
Quote: The most common bell shaped curve is the normal or Gaussian but
not all data forming a symmetrical bell shaped curve are normal.
I wen to Google to search for other bell curves but found none.
http://en.wikipedia.org/wiki/Cauchy_distribution
Han de Bruijn |
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| user923005 |
| Posted: Wed Jan 10, 2007 3:32 pm |
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| Beliavsky |
| Posted: Sun Jan 14, 2007 2:53 pm |
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Stig Holmquist wrote:
Quote: The most common bell shaped curve is the normal or Gaussian but
not all data forming a symmetrical bell shaped curve are normal.
I wen to Google to search for other bell curves but found none
Other commonly-used families of symmetric unimodal distributions are
the Student t (which includes the Cauchy distribution mentioned by
another poster) and the exponential power distribution aka generalized
error distribution (GED). Both families nest the normal distribution,
and the GED also nests the Laplace aka double exponential distribution.
You can search for info on these.
..
Quote: Is there a book discussing other bell curves and how to find
their standard deviation from the mean?
I don't think this can be done. For the normal distribution and the
alternatives I mentioned, the mean and standard deviation are
separately specified parameters.
Btw the best newsgroup for your question was probably sci.stat.math. |
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