TY - JOUR
T1 - On the number and sum of near-record observations
AU - Balakrishnan, N.
AU - Pakes, Anthony
AU - Stepanov, A.
PY - 2005
Y1 - 2005
N2 - Let X-1, X-2,... be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L (n) and X (n) denote the nth record time and the nth record value, respectively. We refer to the variables X-i as near-nth-record observations if X-i epsilon (X (n) - a, X (n)], with a > 0, and L (n) < i < L (n + 1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.
AB - Let X-1, X-2,... be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L (n) and X (n) denote the nth record time and the nth record value, respectively. We refer to the variables X-i as near-nth-record observations if X-i epsilon (X (n) - a, X (n)], with a > 0, and L (n) < i < L (n + 1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.
U2 - 10.1239/aap/1127483746
DO - 10.1239/aap/1127483746
M3 - Article
VL - 37
SP - 765
EP - 780
JO - Advances in Applied Probability (SGSA)
JF - Advances in Applied Probability (SGSA)
SN - 0001-8678
IS - 3
ER -