El-Gayar, S., Anis, A. (1974). On the Mean Range of Partial Sums of a Finite Number of Random Variables. The Egyptian Statistical Journal, 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". The Egyptian Statistical Journal, 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', The Egyptian Statistical Journal, 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. The Egyptian Statistical Journal, 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 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.
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