Are continuous mappings preserving normality necessarily linear?

• Autorzy: Jacek Wesołowski
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

normal distribution; Cauchy distribution; distributions of functions of random variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 1
• Strony: 109-112

Daty

wydano

1996

otrzymano

1996-05-23

Twórcy

autor

Jacek Wesołowski

• Mathematical Institute, Warsaw University of Technology , Plac Politechniki 1, 00-661 Warszawa, Poland

Bibliografia

• B. C. Arnold (1979), Some characterizations of the Cauchy distribution, Austral. J. Statist. 21, 166-169.
• N. L. Johnson, S. Kotz and N. Balakrishnan (1994), Continuous Univariate Distributions, Vol. I, Wiley, New York.
• 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.
• 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.