Zero biasing and a discrete central limit theorem
نویسندگان
چکیده
منابع مشابه
Zero Biasing and a Discrete Central Limit Theorem
We introduce a new family of distributions to approximate IP(W ∈ A) for A ⊂ {· · · ,−2,−1, 0, 1, 2, · · · } and W a sum of independent integer-valued random variables ξ1, ξ2, · · · , ξn with finite second moments, where with large probability W is not concentrated on a lattice of span greater than 1. The well-known Berry–Esseen theorem states that for Z a normal random variable with mean IE(W )...
متن کاملZero Biasing and a Discrete Central Limit Theorem by Larry Goldstein
University of Southern California and University of Melbourne We introduce a new family of distributions to approximate P(W ∈A) for A ⊂ {. . . ,−2,−1,0,1,2, . . .} and W a sum of independent integer-valued random variables ξ1, ξ2, . . . , ξn with finite second moments, where, with large probability, W is not concentrated on a lattice of span greater than 1. The well-known Berry–Esseen theorem s...
متن کاملBerry–esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences, Using Zero and Size Biasing
Berry–Esseen-type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are a...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملA Martingale Central Limit Theorem
We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.
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 Annals of Probability
سال: 2006
ISSN: 0091-1798
DOI: 10.1214/009117906000000250