### Abstract

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.

Original language | English |
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Pages (from-to) | 765-780 |

Journal | Advances in Applied Probability |

Volume | 37 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 |

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## Cite this

Balakrishnan, N., Pakes, A., & Stepanov, A. (2005). On the number and sum of near-record observations.

*Advances in Applied Probability*,*37*(3), 765-780. https://doi.org/10.1239/aap/1127483746