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Titlebook: Generalized Hyperbolic Secant Distributions; With Applications to Matthias J. Fischer Book 2014 The Author(s) 2014 62E15, 62P20, 91G70, 91B

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Hyperbolic Secant Distributions,function, cumulative density function and quantile function, admit simple and closed-form expressions, which makes it appealing from a practical and a theoretical point of view. In particular, HSD can be used as starting distribution to obtain generalized distribution systems which exhibit skewness and heavier (or lighter) tails.
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Savanna and Open-Woodland Communitiesy investigated by Baten (1934) for . followed by Baten’s [.] generalization for arbitrary .. In order to introduce skewness, it was suggested to apply the Esscher transformation afterwards. The resulting distribution is frequently termed as NEF-GHS or Meixner distribution and is the focus of this chapter.
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The NEF-GHS or Meixner Distribution Family,y investigated by Baten (1934) for . followed by Baten’s [.] generalization for arbitrary .. In order to introduce skewness, it was suggested to apply the Esscher transformation afterwards. The resulting distribution is frequently termed as NEF-GHS or Meixner distribution and is the focus of this chapter.
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Mary-Ann Stanley,Owen Lee Griffiths [.–.]. It is symmetric and bell-shaped like the Gaussian distribution but has slightly heavier tails. However, in contrast, both probability density function, cumulative density function and quantile function, admit simple and closed-form expressions, which makes it appealing from a practical and a
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https://doi.org/10.1007/978-981-99-0945-2 . on the real line, we can modify its shape (i.e., introduce skewness and in-/decrease kurtosis) if . is appropriately weighted. In particular, every density . on the interval . is a specific weighting function. In this chapter, we follow up a proposal of Jones [.] and choose the Beta distribution
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