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 -