# Are continuous mappings preserving normality necessarily linear?

Applicationes Mathematicae (1996)

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

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topWesołowski, 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

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

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