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}

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**Abdulhamid A. Alzaid, C. Radhakrishna Rao, and D. N. Shanbhag,*Solution of the integrated Cauchy functional equation on a half line using exchangeability*, Sankhyā Ser. A**49**(1987), no. 2, 189–194. MR**1055782****2**Ka-Sing Lau and C. Radhakrishna Rao,*Integrated Cauchy functional equation and characterizations of the exponential law*, Sankhyā Ser. A**44**(1982), no. 1, 72–90. MR**753078****3**Prem S. Puri and Herman Rubin,*A characterization based on the absolute difference of two i.i.d. random variables*, Ann. Math. Statist.**41**(1970), 2113–2122. MR**0293761****4**B. Ramachandran,*An integral equation in probability theory and its applications*, Indian Statistical Institute, 1980.**5**Balasubrahmanyan Ramachandran and Ka-Sing Lau,*Functional equations in probability theory*, Probability and Mathematical Statistics, Academic Press, Inc., Boston, MA, 1991. MR**1132671****6**C. Radhakrishna Rao,*An extension of Deny’s theorem and its application to characterizations of probability distributions*, A Festschrift for Erich L. Lehmann, Wadsworth Statist./Probab. Ser., Wadsworth, Belmont, CA, 1983, pp. 348–366. MR**689754****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,*Characterization of the exponential and the 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), no. 3, 207–216 (English, with German and Russian summaries). MR**0331583****9**W. Stadje,*A characterization of the exponential distribution involving absolute differences of i.i.d. random variables*, Proc. Amer. Math. Soc.**121**(1994), no. 1, 237–243. MR**1200180**, 10.1090/S0002-9939-1994-1200180-1

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Additional Information

**C. R. Rao**

Email:
crr1@psuvm.psu.edu

DOI:
http://dx.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