[SciPy-User] deterministic random variable

[josef.pktd at gmail.com]

On Mon, May 17, 2010 at 3:57 PM, nicky van foreest <vanforeest at gmail.com> wrote:
> Hi Josef,
>
> Thanks for the answer.
>
>> Actually, if the onepoint distribution directly subclasses rv_generic
>> then it wouldn't rely on or interfere with the generic framework in
>> rv_continuous or rv_discrete (where it wouldn't really fit in if
>> onepoint is on reals), and it might be relatively easy to provide all
>> the methods of the distributions for a single point distribution.
>
> I must admit that I haven't had a look at the innards of rv_generic,
> so I am afraid I cannot be of any relevant help in this respect.
>
>>
>> Choice of name:
>> to me, "deterministic random variable" sounds like an oxymoron,
>> although I found some references to deterministic distribution (mainly
>> or exclusively in queuing theory and
>> http://isi.cbs.nl/glossary/term902.htm)
>> I would prefer a boring "onepoint" distribution, or "degenerate", or ... ?
>
> Degenerate seems nice to me. I just checked the book Probability by
> Shiryaev, and he also uses the word `degenerate'. Interestingly, he
> introduces the degenerate distribution as the normal distribution with
> sigma = 0. I suspect that implementing the degenerate distribution
> like this is utterly stupid.
>
>> Can you file a ticket with what you would like to have?
>
> Sure. Sorry for bothering you with this, but how?

Nicky, Sorry about the delay, another thread I lost track of.

http://projects.scipy.org/scipy/newticket
has a form to fill out, you might have to sign up first
It's a good place to file things so they don't get forgotten.

>
>> <rambling ahead>
>> I started to work again a bit on enhancing the distributions, mainly
>> I'm experimenting with several generic estimation methods. My target
>> is to have a working estimator for any distribution in scipy.stats and
>> for several additional distributions.
>
> This seems a nice idea, but quite ambitious. Have you also thought
> about estimators for heavy tailed distributions? This is, as far as I
> know, a very delicate topic.
>
>>
>> I worry a bit that a deterministic distribution might not fit into a
>> general framework for distributions and might need to be special cased
>> for some methods. (but see above)
>
> This must be fairly easy. Just the mean can be relevant.

We would want to provide all the same methods, even if most of them are trivial.

BTW: I had started to work on the discrete distribution on the real
line. Some methods
works easily, but then I ran into the "hashtable on floats" problem
(from another thread)

pdf(x), cdf(x)  with x float would need to know whether x is a support
point, but which might not be equal to the actual point because of
floating point problems.
So, the direct translation of rv_discrete doesn't work, and it looks
like at least pdf needs to be accessible either pointwise for queries
or using known support points for actual calculations.

No fun, and EDA dropped.

Josef

>
>> http://bazaar.launchpad.net/~josef-pktd/statsmodels/statsmodels-josef-experimental/files/head:/scikits/statsmodels/sandbox/stats/
>
> I'll have a look. Thanks.
>
> Nicky
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