Are continuous mappings preserving normality necessarily linear?

Jacek Wesołowski

Applicationes Mathematicae (1996)

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

Abstract

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

How to cite

top

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

top
  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 ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.