Generalized Hyperbolic Secant Distributions

With Applications to Finance

Business & Finance, Economics, Statistics, Nonfiction, Science & Nature, Mathematics
Cover of the book Generalized Hyperbolic Secant Distributions by Matthias J. Fischer, Springer Berlin Heidelberg
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Author: Matthias J. Fischer ISBN: 9783642451386
Publisher: Springer Berlin Heidelberg Publication: December 20, 2013
Imprint: Springer Language: English
Author: Matthias J. Fischer
ISBN: 9783642451386
Publisher: Springer Berlin Heidelberg
Publication: December 20, 2013
Imprint: Springer
Language: English

​Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally, the Cauchy distribution is also used. Surprisingly, the hyperbolic secant distribution has led a charmed life, although Manoukian and Nadeau had already stated in 1988 that “... the hyperbolic-secant distribution ... has not received sufficient attention in the published literature and may be useful for students and practitioners.” During the last few years, however, several generalizations of the hyperbolic secant distribution have become popular in the context of financial return data because of its excellent fit. Nearly all of them are summarized within this Springer Brief.

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​Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally, the Cauchy distribution is also used. Surprisingly, the hyperbolic secant distribution has led a charmed life, although Manoukian and Nadeau had already stated in 1988 that “... the hyperbolic-secant distribution ... has not received sufficient attention in the published literature and may be useful for students and practitioners.” During the last few years, however, several generalizations of the hyperbolic secant distribution have become popular in the context of financial return data because of its excellent fit. Nearly all of them are summarized within this Springer Brief.

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