A family of bell-shaped distributions built around the hyperbolic secant is devised. Moment and cumulant generating functions are provided leading to closed form representations of moments in terms of polygamma functions. As a by-product the behaviour of kurtosis is investigated showing that it is upperly bounded by six and lowerly bounded by three. The distributions at stake bridge the Laplace and Gaussian laws, both arising as limit distributions.
Zoia, M., Faliva, M., The family of power raised hyperbolic secant distributions: moments kurtosis, limit laws, <<THE FAMILY OF POWER-RAISED HYPERBOLIC SECANTDISTRIBUTIONS: MOMENTS, KURTOSIS, LIMIT LAWS>>, 2014; (Luglio): 1-22 [http://hdl.handle.net/10807/64578]
The family of power raised hyperbolic secant distributions: moments kurtosis, limit laws
Zoia, Maria;Faliva, Mario
2014
Abstract
A family of bell-shaped distributions built around the hyperbolic secant is devised. Moment and cumulant generating functions are provided leading to closed form representations of moments in terms of polygamma functions. As a by-product the behaviour of kurtosis is investigated showing that it is upperly bounded by six and lowerly bounded by three. The distributions at stake bridge the Laplace and Gaussian laws, both arising as limit distributions.
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