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On characterization of certain probability distributions

Published online by Cambridge University Press:  24 October 2008

Y. H. Wang
Y. H. Wang
Affiliation:
Division of Statistics, Ohio State University
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Introduction: Let X1, X2, …, Xn be n (n ≤ 2) independent observations on a random variable X with distribution function F. Also let L = L (X1, X2, …, Xn) be a linear statistic and Q = Q (X1, X2, …, Xn) be a homogeneous quadratic statistic. In this paper, we consider the problem of characterizing a class of probability distributions by the linear regression of the statistic Q on the other statistic L. In section 2, we obtain a characterization of a class of probability distributions, which includes the normal and the Poisson distributions. In section 3, a class of distributions including the gamma, the binomial and the negative binomial distributions is characterized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 347 - 352
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Fisher, R. A.Applications of ‘Student's’ distribution. Metron 5–3 (1925), 90–104.Google Scholar
(2)Geary, R. C.Distribution of ‘Student's’ ratio for non-normal samples. J. Roy. Statist. Soc. Suppl., Ser. B 3 (1936), 178–184.Google Scholar
(3)Kawata, T. and Sakamoto, H.On the characterization of the normal population by the independence of the sample mean and the sample variance. J. Math. Soc. Japan 1 (1949), 111–115.Google Scholar
(4)Laha, R. G.On an extension of Geary's theorem. Biometrika 40 (1953), 228–229.Google Scholar
(5)Lukacs, E.A characterization of the normal distribution. Ann. Math. Statist. 13 (1942), 91–93.Google Scholar
(6)Lukacs, E. Characterization of populations by properties of suitable statistics. Proc. Third Berkeley Symposium on Math. Stat. and Prob. (U. of Calif. Press, Berkeley) (1956), 195–214.Google Scholar
(7)Lukacs, E. Recent developments in the theory of characteristic functions. Proc. Fourth Berkeley Symposium on Math. Stat. and Prob. (U. of Calif. Press, Berkeley) (1960), 307–335.Google Scholar
(8)Shanbhag, D. N.Another characteristic property of the Poisson distribution. Proc. Cambridge Philos. Soc. 68 (1970), 167–169.CrossRefGoogle Scholar
(9)Wang, Y. H. On characterization of some probability distributions and estimation of the parameters of the Pareto distribution. Ph.D. Dissertation, Ohio State University (1971).Google Scholar
(10)Zinger, A. A.On independent samples from normal population. Uspehi Matem. Nauk (N.S.) 6, no. (45) (1951), 172–175.Google Scholar