Jacek Wesołowski (1996)
Applicationes Mathematicae
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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.
Carles M. Cuadras (2002)
Qüestiió
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Advanced calculus is necessary to prove rigorously the main properties of the Cauchy distribution. It is well known that the Cauchy distribution can be generated by a tangent transformation of the uniform distribution. By interpreting this transformation on a circle, it is possible to present elementary and intuitive proofs of some important and useful properties of the distribution.
Berrone, Lucio R. (2005)
International Journal of Mathematics and Mathematical Sciences
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Vanderperre, Edmond J. (2008)
Journal of Applied Mathematics and Stochastic Analysis
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Vanderperre, E.J. (2005)
Mathematical Problems in Engineering
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Marija Skendžić (1970)
Publications de l'Institut Mathématique
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Raetz, Juerg (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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E. J. Vanderperre, S. Vannakrairojn, S.S. Makhanov (1999)
The Yugoslav Journal of Operations Research
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J. Ligęza (1975)
Colloquium Mathematicae
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Fill, James Allen, Janson, Svante (2000)
Electronic Communications in Probability [electronic only]
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I. Kotlarski (1960)
Colloquium Mathematicae
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Mozgawa, Witold (2009)
Beiträge zur Algebra und Geometrie
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Augustynowicz, A. (1997)
Serdica Mathematical Journal
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We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.