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315762

On the Mean Range of Partial Sums of a Finite Number of Random Variables

Article

Last updated: 28 Dec 2024

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Abstract

The problem of determining the mean of the range of partial sums of random variables is important in planning the storage capacity of reservoirs under the assumption of infinite storage capacity. In this paper, new formulae for the mean of the range (and adjusted range) of partial sums of a finite number of exchangeable random variables are given. These formulae are essentially based on a lemma given by Spitzer (1956) concerning the expected value of the maximum of the partial sums. This lemma of Spitzer is established by a simpler proof when the original random variables are independently and symmetrically distributed.

DOI

10.21608/esju.1974.315762

Keywords

Mean Range of Partial Sums, Finite Number of Random Variables, Infinite Storage Capacity

Authors

First Name

S.M.

Last Name

El-Gayar

MiddleName

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Orcid

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First Name

A.A.

Last Name

Anis

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-

Affiliation

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Volume

18

Article Issue

1

Related Issue

43309

Issue Date

1974-06-01

Receive Date

2023-09-03

Publish Date

1974-06-01

Page Start

1

Page End

12

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_315762.html

Detail API

https://esju.journals.ekb.eg/service?article_code=315762

Order

1

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On the Mean Range of Partial Sums of a Finite Number of Random Variables

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Type

Article

Created At

28 Dec 2024