|
A note on a characteristic property based on order statistics
Author(s):
C.
R.
Rao;
D.
N.
Shanbhag
Journal:
Proc. Amer. Math. Soc.
124
(1996),
299-302.
MSC (1991):
Primary {62E10;
Secondary 62E05}
MathSciNet review:
1317047
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is shown that the extended version of the Puri-Rubin result given recently by Stadje (1994) is neither new nor the most general available in the literature.
References:
- 1
- A. Alzaid, C. R. Rao and D. N. Shanbhag, Solution of the integrated Cauchy functional equation using exchangeability, Sankhya A 49 (1987), 189--194, MR 91e:62027.
- 2
- K. S. Lau and C. R. Rao, Integrated Cauchy functional equation and the characterization of the exponential law, Sankhya 44 (1982), 72--90, MR 85j:62012a.
- 3
- P. S. Puri and H. Rubin, A characterization based on the absolute difference of two i.i.d. random variables, Ann. Math. Statist. 41 (1970), 251--255, MR 45:2836.
- 4
- B. Ramachandran, An integral equation in probability theory and its applications, Indian Statistical Institute, 1980.
- 5
- B. Ramachandran and K. S. Lau, Functional equations in probability theory, Academic Press, New York, 1991, MR 93c:60016.
- 6
- C. R. Rao, An extension of Deny's theorem and its application to characterizations of probability distributions, A festschrift for Eric Lehmann, Wadsworth Statist./Probab. Ser., Wadsworth, Belmont, CA, 1983, pp. (348--366), MR 85d:62018.
- 7
- C. R. Rao and D. N. Shanbhag, Choquet-Deny type functional equations with applications to stochastic models, Wiley, New York, 1994.
- 8
- H. J. Rossberg, Characterizations of the exponential and Pareto distributions by means of some properties of the distributions which the differences and quotients of order statistics are subject to", Math. Operationsforsch. Statist. 3 (1972), 207--216, MR 48:9915.
- 9
- W. Stadje, A characterization of the exponential distribution involving absolute differences of i.i.d. random variables, Proc. Amer. Math. Soc. 121 (1994), 237--243, MR 94g:62022.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
{62E10,
62E05}
Retrieve articles in all Journals with
MSC (1991):
{62E10,
62E05}
Additional Information:
C.
R.
Rao
Affiliation:
Center for Multivariate Analysis, 417 Classroom Building, Penn State University, University Park, Pennsylvania 16802
Email:
crr1@psuvm.psu.edu
D.
N.
Shanbhag
Affiliation:
Department of Probability and Statistics, University of Sheffield, Sheffield S37RH, United Kingdom
DOI:
10.1090/S0002-9939-96-03273-X
PII:
S 0002-9939(96)03273-X
Keywords:
Integrated Cauchy function equation,
Lau-Rao theorem,
order statistics
Received by editor(s):
August 18, 1994
Additional Notes:
Research sponsored by the Army Research Office under Grant DAAHO4-93-G-0030.
Communicated by:
Richard Durrett
Copyright of article:
Copyright
1996,
American Mathematical Society
|
