# Unimodality of the distribution of record statistics

Research output: Contribution to journalArticle

7 Citations (Scopus)

### Abstract

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.

Original language English (US) 395-398 4 Statistics and Probability Letters 56 4 https://doi.org/10.1016/S0167-7152(02)00028-7 Published - Feb 15 2002

### Fingerprint

Record Statistics
Unimodality
Continuous Distributions
Absolutely Continuous
Order Statistics
Identically distributed
Continuous Function
Distribution Function
Random variable
Denote
Statistics

### All Science Journal Classification (ASJC) codes

• Statistics, Probability and Uncertainty
• Statistics and Probability

### Cite this

@article{b8943abbb1864efdbca7fc75d166ed22,
title = "Unimodality of the distribution of record statistics",
abstract = "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.",
author = "Prasanta Basak and Indrani Basak",
year = "2002",
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day = "15",
doi = "10.1016/S0167-7152(02)00028-7",
language = "English (US)",
volume = "56",
pages = "395--398",
journal = "Statistics and Probability Letters",
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publisher = "Elsevier",
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}

In: Statistics and Probability Letters, Vol. 56, No. 4, 15.02.2002, p. 395-398.

Research output: Contribution to journalArticle

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.

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

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

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EP - 398

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

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