A note on a characteristic property based on order statistics
Authors:
C. R. Rao and D. N. Shanbhag
Journal:
Proc. Amer. Math. Soc. 124 (1996), 299302
MSC (1991):
Primary {62E10; Secondary 62E05}
MathSciNet review:
1317047
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Abstract 
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Additional Information
Abstract: It is shown that the extended version of the PuriRubin result given recently by Stadje (1994) is neither new nor the most general available in the literature.
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 A. Alzaid, C. R. Rao and D. N. Shanbhag, Solution of the integrated Cauchy functional equation using exchangeability, Sankhya A 49 (1987), 189194, 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), 7290, MR 85j:62012a.
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 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), 251255, MR 45:2836.
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 B. Ramachandran, An integral equation in probability theory and its applications, Indian Statistical Institute, 1980.
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 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. (348366), MR 85d:62018.
 7
 C. R. Rao and D. N. Shanbhag, ChoquetDeny type functional equations with applications to stochastic models, Wiley, New York, 1994.
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 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), 207216, MR 48:9915.
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 W. Stadje, A characterization of the exponential distribution involving absolute differences of i.i.d. random variables, Proc. Amer. Math. Soc. 121 (1994), 237243, MR 94g:62022.
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Additional Information
C. R. Rao
Email:
crr1@psuvm.psu.edu
DOI:
http://dx.doi.org/10.1090/S000299399603273X
PII:
S 00029939(96)03273X
Keywords:
Integrated Cauchy function equation,
LauRao theorem,
order statistics
Received by editor(s):
August 18, 1994
Additional Notes:
Research sponsored by the Army Research Office under Grant DAAHO493G0030.
Communicated by:
Richard Durrett
Article copyright:
© Copyright 1996
American Mathematical Society
