### 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 | |

State | Published - Feb 15 2002 |

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### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

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*Statistics and Probability Letters*, vol. 56, no. 4, pp. 395-398. https://doi.org/10.1016/S0167-7152(02)00028-7

**Unimodality of the distribution of record statistics.** / Basak, Prasanta; Basak, Indrani.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Unimodality of the distribution of record statistics

AU - Basak, Prasanta

AU - Basak, Indrani

PY - 2002/2/15

Y1 - 2002/2/15

N2 - Let X1,X2,..., 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 X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(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.

AB - Let X1,X2,..., 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 X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(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.

UR - http://www.scopus.com/inward/record.url?scp=0037082550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037082550&partnerID=8YFLogxK

U2 - 10.1016/S0167-7152(02)00028-7

DO - 10.1016/S0167-7152(02)00028-7

M3 - Article

AN - SCOPUS:0037082550

VL - 56

SP - 395

EP - 398

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -