On the Mean Range of Partial Sums of a Finite Number of Random Variables
El-Gayar, S., Anis, A. (1974). On the Mean Range of Partial Sums of a Finite Number of Random Variables. EKB Journal Management System, 18(1), 1-12. doi: 10.21608/esju.1974.315762
S.M. El-Gayar; A.A. Anis. "On the Mean Range of Partial Sums of a Finite Number of Random Variables". EKB Journal Management System, 18, 1, 1974, 1-12. doi: 10.21608/esju.1974.315762
El-Gayar, S., Anis, A. (1974). 'On the Mean Range of Partial Sums of a Finite Number of Random Variables', EKB Journal Management System, 18(1), pp. 1-12. doi: 10.21608/esju.1974.315762
El-Gayar, S., Anis, A. On the Mean Range of Partial Sums of a Finite Number of Random Variables. EKB Journal Management System, 1974; 18(1): 1-12. doi: 10.21608/esju.1974.315762

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

The Egyptian Statistical Journal
Article 1, Volume 18, Issue 1, June 1974, Page 1-12  XML
Document Type: Original Article
DOI: 10.21608/esju.1974.315762
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Authors
S.M. El-Gayar; A.A. Anis
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.
Keywords
Mean Range of Partial Sums; Finite Number of Random Variables; Infinite Storage Capacity
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