Does anybody know what the heck 'uncorrelated multivariate Poisson distribution' means?
It depends whether you're referring to a specific uncorrelated multivariate Poisson distribution, or any uncorrelated multivariate Poisson distribution.
Rover
You have answered your own question here, and below.It is actually simple. A distribution is a function. A function is a procedure for computing something from something else. In this particualr case you feed in intereger values to such function and get out values from zero to one (probabilities). A Multivariate function is a product of such functions. The real problem is elswehere. It is about whether to treat a set of functions as countable or uncountable.
No. Poisson distribution, like any distribution, as a way of distributing, may be uncountable, but of you have a set of Poisson distributions, then it is coutable. Real numbers can be counted, surely?I never understood this part, I have to be honest, whether "distribution" is countable or uncountable. A distribution, being a function, or an object if you wish, is parameterized by parameters. They can be real numbers (uncountable), or integers (countable).
My understanding is that an English speaking person would see the Poission distribution, which is parameterized by one real number, as an uncountable object (like sugar, water, etc). Real numbers cannot be counted, so I would expect that the set/class of all Poission distributions is uncountable. It should be either with the or without it.
No. Boyle's Law, Fermat's Last Theorem, Einstein's Theory of Relativity.But then in academic writing one has to use "the" (the definite article in front of a proper noun rule I think?).
Well, presumably if you can have a multivariate Poisson distribution, you can have a non-multivariate one.Thus Saying "the Poisson distribution" is common. I wonder whether one can say "a Poisson distribution"? I wonder whether adding adjectives in front changes also what one has to use e.g. "multivariate Poisson distribution".
I can't count them. I hear Chuck Norris is in the business of counting elements of infinite sets.Real numbers can be counted, surely?
"Poisson" may mean fish in French, but Siméon-Denis Poisson wasn't a fish."Poisson" is French for fish, but what the text means and why it should mix French and English I can't imagine.
Probability distributions are countable in the grammatical sense. Real numbers' being uncountable and natural numbers' being countable in the set-theoretic sense has nothing to do with it. Real numbers are countable grammatically, which is proven by the fact that this sentence is correct.I have to be honest, whether "distribution" is countable or uncountable.
BC!I'm not suspicious usually but I'm starting to suspect your questions aren't honest.
Yes.I wonder whether one can say "a Poisson distribution"?
Well, presumably if you can have a multivariate Poisson distribution, you can have a non-multivariate one.
Yes.
I'm not suspicious usually but I'm starting to suspect your questions aren't honest.
There are 131,000 examples of "a Poisson distribution" in Google Scholar.
Zorank, I think Google Scholar could be a simple way to test the acceptability of technical phrases. It may not be perfect, but the sources are sound, and if you get a result like that, then it's clearly in use in academic and technical writing.
Probability distributions are countable in the grammatical sense. Real numbers' being uncountable and natural numbers' being countable in the set-theoretic sense has nothing to do with it. Real numbers are countable grammatically, which is proven by the fact that this sentence is correct.
...an English-language ... mathematics forum...
It's OK to say. But those are irrational numbers you speak of. They have an infinite number of decimal digits.
2.5 and 3.0 are real numbers, but they can be expressed perfectly with a finite number of digits.
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