Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-30T06:34:19.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of distributions by the identical distribution of linear forms

Published online by Cambridge University Press:  14 July 2016

Morris L. Eaton
Morris L. Eaton*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper, we shall write ℒ(W) = ℒ(Z) to mean the random variables W and Z have the same distribution. The relation “ℒ(W) = ℒ(;Z)” reads “the law of W equals the law of Z”.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 481 - 494
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Blum, J. R. (1956) On a characterization of the normal distribution. Skand. Aktuarietidskr. 59–62.CrossRefGoogle Scholar
[2] Cramer, H. (1937) Random Variables and Probability Distributions. The University Press, Cambridge.Google Scholar
[3] Gnedenko, B. V. and Kolmogorov, A. N. (1954) Limit Distributions for Sums of Independent Random Variables. Addison Wesley, Reading, Mass.Google Scholar
[4] Laha, R. G. and Lukacs, E. (1965) On a linear form whose distribution is identical with that of a monomial. Pacific J. Math. 15, 207–214.CrossRefGoogle Scholar
[5] Levy, P. (1937) Théorie de l'Addition des Variables Aléatoires. Gauthier-Villars, Paris.Google Scholar
[6] Linnik, Yu. V. (1963) Linear forms and statistical criteria, I, II. Selected Translations in Mathematical Statistics and Probability. 3, 1–40 and 41–90.Google Scholar
[7] Lukacs, E. (1956) Characterization of populations by properties of suitable statistics. Proc. Third Berkeley Symp. Math. Statist. Prob. 2, 195–214. Univ. of California Press.Google Scholar
[8] Marcinkiewicz, J. (1939) Sur une propriété de la loi de Gauss. Math. Z., 44, 612–618.CrossRefGoogle Scholar
[9] Niven, I. (1963) Diophantine Approximations. Interscience tracts in pure and applied mathematics, Number 14, Interscience, New York.Google Scholar