TY - JOUR
T1 - Limit laws for the number of near-maxima via the Poisson approximation
AU - Pakes, Anthony
AU - Li, Y.
PY - 1998
Y1 - 1998
N2 - Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n --> infinity. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing with respect to extreme value laws. For the case of attraction to the Frechet law, the effects of relaxing a technical condition are examined. The results are set in the broader context of counting observations near upper order statistics. This involves little extra effort. (C) 1998 Elsevier Science B.V. All rights reserved.
AB - Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n --> infinity. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing with respect to extreme value laws. For the case of attraction to the Frechet law, the effects of relaxing a technical condition are examined. The results are set in the broader context of counting observations near upper order statistics. This involves little extra effort. (C) 1998 Elsevier Science B.V. All rights reserved.
U2 - 10.1016/S0167-7152(98)00148-5
DO - 10.1016/S0167-7152(98)00148-5
M3 - Article
VL - 40
SP - 395
EP - 401
JO - Statistics & Probability Letters
JF - Statistics & Probability Letters
ER -