Unimodality of the distribution of record statistics

Prasanta Basak; Indrani Basak

doi:10.1016/S0167-7152(02)00028-7

Unimodality of the distribution of record statistics

Prasanta Basak, Indrani Basak

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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,...,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)
Pages (from-to)	395-398
Number of pages	4
Journal	Statistics and Probability Letters
Volume	56
Issue number	4
DOIs	https://doi.org/10.1016/S0167-7152(02)00028-7
State	Published - Feb 15 2002

All Science Journal Classification (ASJC) codes

Statistics, Probability and Uncertainty
Statistics and Probability

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10.1016/S0167-7152(02)00028-7

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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.",

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

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

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ER -

Unimodality of the distribution of record statistics

Abstract

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