Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-30T08:05:16.930Z Has data issue: false hasContentIssue false
  • English
  • Français

On the expected range and expected adjusted range of partial sums of exchangeable random variables

Published online by Cambridge University Press:  14 July 2016

D. C. Boes  and
J.D. Salas-La Cruz
D. C. Boes
Affiliation:
Colorado State University, Fort Collins
Get access Rights & Permissions [Opens in a new window]

Abstract

Studies of storage capacity of reservoirs, under the assumption of infinite storage, lead to the problem of finding the distribution of the range or adjusted range of partial sums of random variables.

In this paper, formulas for the expected values of the range and adjusted range of partial sums of exchangeable random variables are presented. Such formulas are based on an elegant result given in Spitzer (1956). Some consequences of the aforementioned formulas are discussed.

Keywords

EXPECTED ADJUSTED RANGE OF PARTIAL SUMS OF EXCHANGEABLE RANDOM VARIABLESADJUSTED RANGE IN STORAGE THEORYHURST PHENOMENONSTABLE DISTRIBUTIONS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 671 - 677
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Research supported by the National Science Foundation, Grant No. GK-31512X.

References

Anis, A. A. and Lloyd, E. H. (1953) On the range of partial sums of a finite number of independent random variates. Biometrika 40, 35–42.10.1093/biomet/40.1-2.35Google Scholar
Feller, W. (1951) The asymptotic distribution of the range of sums of independent variables. Ann. Math. Statist. 22, 427–432.10.1214/aoms/1177729589Google Scholar
Hurst, H. E. (1951) Long term storage capacities of reservoirs. Trans. Amer. Soc. Civil Engineers 116, 776–808.10.1061/TACEAT.0006518Google Scholar
Moran, P. A. P. (1964) On the range of cumulative sums. Ann. Inst. Statist. Math. (Tokyo) 16, 109–112.10.1007/BF02868565Google Scholar
Salas-La Cruz, J. D. (1972) Range Analysis for Storage Problems of Periodic-Stochastic Processes. Ph.D. Dissertation, Colorado State University, Fort Collins, Colorado.Google Scholar
Solari, M. E. and Anis, A. A. (1957) The mean and variance of the maximum of the adjusted partial sums of a finite number of independent normal variates. Ann. Math. Statist. 28, 706–716.10.1214/aoms/1177706882Google Scholar
Spitzer, F. (1956) A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82, 323–339.10.1090/S0002-9947-1956-0079851-XGoogle Scholar