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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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