Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T13:02:43.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Relationships between order statistics and record values and some characterization results

Published online by Cambridge University Press:  14 July 2016

Ramesh C. Gupta
Ramesh C. Gupta*
Affiliation:
University of Maine at Orono
*
∗ Present address: Biomathematics Modeling Branch (SAM/BR), USAF School of Aerospace Medicine, Brooks AFB, TX 78235, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The similarity between order statistics and record values motivated us, in this paper, to investigate some relationships between the order statistics and the record values. These relationships are employed to characterize a continuous distribution by some moment properties of the spacings of the record values, and hence obtain characterizations of the exponential distribution. Some of the well-known results follow trivially.

Keywords

EXPONENTIAL DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 425 - 430
Copyright
Copyright © Applied Probability Trust 1984 

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

Ahsanullah, M. (1978) Record values and the exponential distribution. Ann. Inst. Statist. Math. 30, 429–433.CrossRefGoogle Scholar
Ahsanullah, M. (1979) Characterization of the exponential distribution by record values. Sankhya B 41, 116–121.Google Scholar
Ahsanullah, M. (1980) Linear prediction of record values for the two parameter exponential distribution. Ann. Inst. Statist. Math. 32, 363–368.CrossRefGoogle Scholar
Ahsanullah, M. (1981a) Record values of exponentially distributed random variables. Statist. Hefte 22 (2), 121–127.CrossRefGoogle Scholar
Ahsanullah, M. (1981b) On a characterization of the exponential distribution by weak homoscedasticity of record values. Biom. J. 23, 715–717.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability. Holt, Rinehart and Winston, New York.Google Scholar
Bellman, R. and Cooke, K. L. (1963) Differential-Difference Equations. Academic Press, New York.Google Scholar
Chandler, K. N. (1952) The distribution and frequency of record values. J. R. Statist. Soc. B 14, 220–228.Google Scholar
Dallas, A. C. (1981a) Record values and the exponential distribution. J. Appl. Prob. 18, 949–951.CrossRefGoogle Scholar
Dallas, A. C. (1981b) A characterization using conditional variance. Metrika 28, 151–153.CrossRefGoogle Scholar
Deheuvels, P. (1984) The characterization of distributions by order statistics and record values — a unified approach. J. Appl. Prob. 21, 326–334.CrossRefGoogle Scholar
Ferguson, T. S. (1967) On characterizing distributions by properties of order statistics. Sankhya A 29, 265–278.Google Scholar
Galambos, J. (1975) Characterizations of probability distributions by properties of order statistics. In Statistical Distributions in Scientific Work, ed. Patil, G. P., Kotz, S. and Ord, K., Reidel, Dordrecht, 3, 71–88.Google Scholar
Kirmani, S. N. U. A. and Beg, M. I. (1983) On characterization of distributions by expected records. Sankya A.Google Scholar
Nagaraja, H. N. (1977) On a characterization based on record values. Austral. J. Statist. 19, 70–73.CrossRefGoogle Scholar
Nagaraja, H. N. (1978) On the expected values of record values. Austral. J. Statist. 20, 176–182.CrossRefGoogle Scholar
Neuts, M. F. (1967) Waiting times between record observations. J. Appl. Prob. 4, 206–208.CrossRefGoogle Scholar
Pfeifer, D. (1982) Characterizations of exponential distributions by independent non-stationary record increments. J. Appl. Prob. 19, 127–135 (correction p. 906).CrossRefGoogle Scholar
Shorrock, R. W. (1972a). A limit theorem for inter-record times. J. Appl. Prob. 9, 219–233.CrossRefGoogle Scholar
Shorrock, R. W. (1972b) On record values and record times. J. Appl. Prob. 9, 316–326.CrossRefGoogle Scholar
Shorrock, R. W. (1973) Record values and inter-record times. J. Appl. Prob. 10, 543–555.CrossRefGoogle Scholar
Siddiqui, M. M. and Biondini, R. W. (1975) The joint distribution of record values and inter-record times. Ann. Prob. 3, 1012–1013.CrossRefGoogle Scholar
Springer, M. D. (1979) Algebra of Random Variables. Wiley, New York.Google Scholar
Srivastava, R. C. (1978) Some characterizations of the exponential distribution based on record values. Ohio State University, Tech. Report 170.Google Scholar
Srivastava, R. C. (1981) Some characterizations of the exponential distribution based on record values. In Statistical Distributions in Scientific Work, ed. Taillie, C., Patil, G. P. and Baldessari, B., Reidel, Dordrecht, 4, 411–416.CrossRefGoogle Scholar
Taillie, C. (1981) A note on Srivastava's characterization of the exponential distribution based on record values. In Statistical Distributions in Scientific Work, ed. Taillie, C., Patil, G. P. and Baldessari, B., Reidel, Dordrecht, 4, 417–418.CrossRefGoogle Scholar