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), 299-302

MSC (1991):
Primary {62E10; Secondary 62E05}

DOI:
https://doi.org/10.1090/S0002-9939-96-03273-X

MathSciNet review:
1317047

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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.

**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**.

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Additional Information

**C. R. Rao**

Email:
crr1@psuvm.psu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03273-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

Article copyright:
© Copyright 1996
American Mathematical Society