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Topic: Probabilities not in [0,1]?
Replies: 8   Last Post: Mar 12, 2013 10:56 PM

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 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Probabilities not in [0,1]?
Posted: Mar 12, 2013 10:56 PM

On Mar 12, 4:50 pm, FredJeffries <fredjeffr...@gmail.com> wrote:
> On Mar 10, 11:36 am, "Peter Percival" <peterxperci...@hotmail.com>
> wrote:
>

> > Is there a theory of probability in which probabilities do not lie in the
> > real interval [0,1]?

>
> http://arxiv.org/abs/0912.4767
>

> > More specifically, is there one in which the "space"
> > of probabilities may have points x, y, z with x < y, x < z but y and z not
> > necessarily comparable?

>
> Not sure what you mean by "not necessarily comparable", but in the
> system of smooth infinitesimal analysis we have that if y and z differ
> by an infinitesimal then the order relation does not satisfy the
> trichotomy law:
> (y < z)  OR (y < z) OR (y = z)
>
> http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysishttp://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf

If the infinitesimals of SIA haven't trichotomy, is there at least
that a <= b or b <= a?

Then back to probabilities, it is rather nonstandard (and not with
regards to the standardization of a distribution's parameter) in
probability for a probability to not be within R_[0,1], with that the
sum or integral of the mass/density function over the support space is
one. (Bose/Fermi, parastatistics, anyonic)

https://en.wikipedia.org/wiki/Identical_particles

Regards,

Ross Finlayson