Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T11:58:10.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Some peculiarities of exponential random variables

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Nelly Litvak
Nelly Litvak*
Affiliation:
EURANDOM
*
∗ Postal address: EURANDOM, PO Box 513, 5600 MB, Eindhoven, The Netherlands. Email address: litvak@eurandom.tue.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we utilize a particular transformation of i.i.d. exponential random variables to derive two distributional identities. Throughout the analysis we discover some peculiar properties of exponentials. We also discuss possible generalizations and applications of the results.

Keywords

Partial sumsmemory-less property

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 90B99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 787 - 792
Copyright
Copyright © by the Applied Probability Trust 2001 

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.)

References

Ali, M. M., and Obaidullah, M. (1982). Distribution of linear combination of exponential variates. Commun. Statist. Theory Meth. 11, 1453–1463.CrossRefGoogle Scholar
Azlarov, T. A., and Volodin, N. A. (1986). Characterization problems associated with the exponential distribution. Springer, Berlin.Google Scholar
Bartholdi, J. J. III, and Platzman, L. K. (1986). Retrieval strategies for a carousel conveyor. IIE Trans. 18, 166–173.CrossRefGoogle Scholar
Dimitrov, B., and Khalil, Z. (1990). On a new characterization of the exponential distribution related to a queueing system with an unrealiable server. J. Appl. Prob. 27, 221–226.Google Scholar
Gilat, D. (1994). On a curious property of the exponential ditribution. In Proc. 12th Prague Conf. Information, Statistical Decision Functions and Random Processes, eds Lachout, P. and Višek, J. Á., pp. 77–80.Google Scholar
Litvak, N., and Adan, I. (2001). The travel time in carousel systems under the nearest item heuristic. J. Appl. Prob. 38, 45–54.Google Scholar
Litvak, N., Adan, I., Wessels, J., and Zijm, W. H. M. (2001). Order picking in carousel systems under the nearest item heuristic. Prob. Eng. Inf. Sci. 15, 135–164.Google Scholar
Pyke, R. (1965). Spacings. J. R. Statist. Soc. B 27, 395–436.Google Scholar
Van Harn, K., and Steutel, F. W. (1991). On a characterization of the exponential distribution. J. Appl. Prob. 28, 947–949.Google Scholar
Wilf, H. S. (1987). The exponential distribution. Amer. Math. Monthly 94, 515–518.Google Scholar