Are continuous mappings preserving normality necessarily linear?

Jacek Wesołowski

Applicationes Mathematicae (1996)

  • Volume: 24, Issue: 1, page 109-112
  • ISSN: 1233-7234

Abstract

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An example of a normal nonlinear continuous function of a normal random variable is given. Also the Cauchy case is considered.

How to cite

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Wesołowski, Jacek. "Are continuous mappings preserving normality necessarily linear?." Applicationes Mathematicae 24.1 (1996): 109-112. <http://eudml.org/doc/219147>.

@article{Wesołowski1996,
abstract = {An example of a normal nonlinear continuous function of a normal random variable is given. Also the Cauchy case is considered.},
author = {Wesołowski, Jacek},
journal = {Applicationes Mathematicae},
keywords = {normal distribution; Cauchy distribution; distributions of functions of random variables},
language = {eng},
number = {1},
pages = {109-112},
title = {Are continuous mappings preserving normality necessarily linear?},
url = {http://eudml.org/doc/219147},
volume = {24},
year = {1996},
}

TY - JOUR
AU - Wesołowski, Jacek
TI - Are continuous mappings preserving normality necessarily linear?
JO - Applicationes Mathematicae
PY - 1996
VL - 24
IS - 1
SP - 109
EP - 112
AB - An example of a normal nonlinear continuous function of a normal random variable is given. Also the Cauchy case is considered.
LA - eng
KW - normal distribution; Cauchy distribution; distributions of functions of random variables
UR - http://eudml.org/doc/219147
ER -

References

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  1. B. C. Arnold (1979), Some characterizations of the Cauchy distribution, Austral. J. Statist. 21, 166-169. Zbl0446.62016
  2. N. L. Johnson, S. Kotz and N. Balakrishnan (1994), Continuous Univariate Distributions, Vol. I, Wiley, New York. Zbl0811.62001
  3. I. I. Kotlarski (1967), Problem 6164, Amer. Math. Monthly 84, 575. 
  4. M. F. Neuts (1979), Cauchy random variables, ( Solution to problem 6164), ibid. 86, 229. 
  5. E. J. G. Pitman and E. J. Williams (1967), Cauchy-distributed functions of Cauchy variates, Ann. Math. Statist. 38, 916-918. Zbl0201.51104
  6. L. Shepp (1964), Normal functions of normal random variables, SIAM Rev. 6, 459-460. 
  7. E. J. Williams (1969), Cauchy-distributed functions and a characterization of the Cauchy distribution, Ann. Math. Statist. 40, 1083-1085. Zbl0184.22602

NotesEmbed ?

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