Summation of p.d.f. from any discrete distribution are always 1, where its fulfill the law of a probability. But when we have a discrete uniform distribution with infinite parameter space. Does the summation is also 1? Or is it an improper p.d.f. where it's sum to infinite?
Considering the definition of a discrete uniform distribution with parameters a and b, I do not believe that an infinite parameter space is possible. The probability mass function (pmf, not pdf) is given by 1/n, where n = b-a+1. If b and/or a is (negative) infinity, n would also be infinity and then the pmf would be dividing by infinity. Mathematically, this would be equal to 0 in the limit; not something you want a pmf to be.
I think there must be some confusion between the 'parameter' and 'sample' spaces.
A uniform distribution on [a, b] has an infinite parameter space: all possible values of a and all b > a.
But an infinite sample space would result from a = -infinity or b = infinity or both.
Rianne is right, we cannot get a total probability of 1, this would give an improper distribution with an infinite sum. Its only use, as far as I know, is in Bayesian statistics.
Hi Mario ! ...by definition, proper uniform distributions, continues or discrete, belong to finite supports only. If you try to use UD to model some data sets with infinite range of values, then you can put some initial acceptable limits on the data values to obtain proper UD. Further you can vary these limits to see how your model behaves ...have fun !! :)))
Discrete uniform distribution has a finite support. The question seems to be wrong.
More clarity is required.
First thing in discrete case we use PMF not PDF. Seconly for uniform distribution(either discrete of continuous) Parameter can take finite value only. If not then your variable is not uniform.
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