### Abstract

Let X_{1},X_{2},..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X_{1},X_{2},...,X_{n} by X_{1,n} ≤ ... X_{n,n}. Define L(1) = 1, L(n+1) = min{j: j > L(n), X_{j} > X_{j-1,j-1}}, and X(n) = X_{L(n),L(n)}, n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.

Original language | English (US) |
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Pages (from-to) | 395-398 |

Number of pages | 4 |

Journal | Statistics and Probability Letters |

Volume | 56 |

Issue number | 4 |

DOIs | |

Publication status | Published - Feb 15 2002 |

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### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Statistics and Probability