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Topic: Continuous and discrete uniform distributions of N
Replies: 27   Last Post: Dec 28, 2012 9:45 PM

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FredJeffries@gmail.com

Posts: 1,024
Registered: 11/29/07
Re: Continuous and discrete uniform distributions of N
Posted: Dec 21, 2012 11:23 AM
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On Dec 19, 10:12 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
wrote:
> In the consideration of what a uniform probability distribution over
> the natural integers would be, we can begin as modeling it with real
> functions, basically as the Dirac delta defined not just at zero, but
> at each natural integer, scaled or divided by the number of integers,
> with commensurate width, preserving the properties of a p.d.f. that
> it's everywhere greater than or equal to zero and less than or equal
> to one, and that its area or integral evaluates to one.
>
> Then, where Dirac's delta is described as a spike to infinity at zero
> with unit area, then to have a spike to one at each natural integer,
> basically dividing the spike fairly among the natural integers, the
> consideration then is in as to whether that still would have area one,
> besides that each of the points would have f(x)=1.  (Of course this is
> all modeled standardly with real functions.)  Yet, it has area two
> (exactly because the integral of EF = 1).
>
> Another notion of what would be the nearest analog to a uniform
> probability distribution over the entire set of naturals would be for
> each to have probability 1/omega, that as a discrete instead of
> continuous distribution, the sum over them equals one.  Here then
> there's a consideration that there is a continuous distribution, of N,
> because a p.d.f. exists and a p.d.f. (or CDF) defines a continuous
> distribution.  Then there's also a consideration that there's a
> discrete distribution, of N, defined as one iota for each.
>
>         EF: continuous uniform distribution of N
>         (EF + REF)/2: continuous uniform distribution of N
>         f(x)=iota: discrete uniform distribution of N


You still ain't never caught a rabbit.

Dirac delta, infinitesimals, irrational numbers, transfinite
ordinals, ... are legitimate not because they have been rigorously
defined but because they can be used to SOLVE PROBLEMS. See, for
instance, Jesper Lützen's "The Prehistory of the Theory of
Distributions"
http://books.google.com/books?id=pC7vAAAAMAAJ

No one has ever anywhere actually used the concept of a uniform
distributions on N to solve any problem.

You can't even show how to use it to calculate the area of a triangle.



>
> Regards,
>
> Ross Finlayson




Date Subject Author
12/20/12
Read Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/21/12
Read Re: Continuous and discrete uniform distributions of N
FredJeffries@gmail.com
12/21/12
Read Re: Continuous and discrete uniform distributions of N
Bill Taylor
12/22/12
Read Re: Continuous and discrete uniform distributions of N
Porky Pig Jr
12/22/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/24/12
Read Re: Continuous and discrete uniform distributions of N
FredJeffries@gmail.com
12/22/12
Read Re: Continuous and discrete uniform distributions of N
David Bernier
12/22/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/24/12
Read Re: Continuous and discrete uniform distributions of N
FredJeffries@gmail.com
12/24/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/26/12
Read Re: Continuous and discrete uniform distributions of N
gus gassmann
12/26/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide
12/27/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/27/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/28/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/28/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/28/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/28/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/28/12
Read Re: Continuous and discrete uniform distributions of N
Virgil
12/28/12
Read Re: Continuous and discrete uniform distributions of N
ross.finlayson@gmail.com
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Shmuel (Seymour J.) Metz
12/25/12
Read Re: Continuous and discrete uniform distributions of N
Butch Malahide

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