The smallest upper bound for thepth absolute central moment of a class of random variables

Martín Egozcue; Luis Fuentes García; Wing-Keung Wong; Ričardas Zitikis

The smallest upper bound for the^pth absolute central moment of a class of random variables

Martín Egozcue^*
, Luis Fuentes García
, Wing-Keung Wong
, Ričardas Zitikis

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

8 Citations (Scopus)

Abstract

We establish the smallest upper bound for the pth absolute central moment over the class of all random variables with values in a compact interval. Numerical values of the bound are calculated for the first ten integer values of p, and its asymptotic behaviour derived when p tends to infinity. In addition, we establish an analogous bound in the case of all symmetric random variables with values in a compact interval. Such results play a role in a number of areas including actuarial science, economics, finance, operations research, and reliability.

Original language	English
Pages (from-to)	125-131
Number of pages	7
Journal	Mathematical Scientist
Volume	37
Issue number	2
Publication status	Published - Dec 2012

User-Defined Keywords

Central moment
Convex function
Edmundson-Madansky bound
Mean
Smallest upper bound

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https://www.appliedprobability.org/publications/the-mathematical-scientist

Cite this

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abstract = "We establish the smallest upper bound for the pth absolute central moment over the class of all random variables with values in a compact interval. Numerical values of the bound are calculated for the first ten integer values of p, and its asymptotic behaviour derived when p tends to infinity. In addition, we establish an analogous bound in the case of all symmetric random variables with values in a compact interval. Such results play a role in a number of areas including actuarial science, economics, finance, operations research, and reliability.",

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AU - Egozcue, Martín

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AU - Wong, Wing-Keung

AU - Zitikis, Ričardas

PY - 2012/12

Y1 - 2012/12

N2 - We establish the smallest upper bound for the pth absolute central moment over the class of all random variables with values in a compact interval. Numerical values of the bound are calculated for the first ten integer values of p, and its asymptotic behaviour derived when p tends to infinity. In addition, we establish an analogous bound in the case of all symmetric random variables with values in a compact interval. Such results play a role in a number of areas including actuarial science, economics, finance, operations research, and reliability.

AB - We establish the smallest upper bound for the pth absolute central moment over the class of all random variables with values in a compact interval. Numerical values of the bound are calculated for the first ten integer values of p, and its asymptotic behaviour derived when p tends to infinity. In addition, we establish an analogous bound in the case of all symmetric random variables with values in a compact interval. Such results play a role in a number of areas including actuarial science, economics, finance, operations research, and reliability.

KW - Central moment

KW - Convex function

KW - Edmundson-Madansky bound

KW - Mean

KW - Smallest upper bound

UR - https://www.scopus.com/pages/publications/84871867446

M3 - Journal article

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EP - 131

JO - Mathematical Scientist

JF - Mathematical Scientist

IS - 2

ER -

The smallest upper bound for the^pth absolute central moment of a class of random variables

Abstract

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