Convergence in Distribution for Subset Counts Between Random Sets
نویسندگان
چکیده
منابع مشابه
Convergence in Distribution for Subset Counts Between Random Sets
Erdős posed the problem of how many random subsets need to be chosen from a set of n elements, each element appearing in each subset with probability p = 1/2, in order that at least one subset is contained in another. Rényi answered this question, but could not determine the limiting probability distribution for the number of subset counts because the higher moments diverge to infinity. The mod...
متن کاملSome Results on Convergence in Distribution for Fuzzy Random Sets
In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and uppersemicontinuous fuzzy sets with compact support in Rp. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.
متن کاملRandom Set Partitions: Asymptotics of Subset Counts
We study the asymptotics of subset counts for the uniformly random partition of the set [n]. It is known that typically most of the subsets of the random partition are of size r, with re=n. Confirming a conjecture formulated by Arratia and Tavare , we prove that the counts of other subsets are close, in terms of the total variation distance, to the corresponding segments of a sequence [Zj] of i...
متن کاملWeak Convergence of Random Sets
In this paper the classical Portmanteau theorem which provides equivalent conditions of weak convergence of sequence of probability measures is extended on the space of the sequence of probability measures induced by random sets.
متن کاملConvergence in Distribution for Uncertain Random Variables
A random variable is a measurable function from an uncertainty space to the set of real numbers, which is used to model randomness. An uncertain variable is a measurable function from uncertainty space to the set of real numbers, which is used to describe uncertainty. However, randomness and uncertainty often simultaneously appear in a complex system. Uncertain random variable provides a useful...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1812