A Distribution Family Bridging the Gaussian and the Laplace Laws, Gram–Charlier Expansions, Kurtosis Behaviour, and Entropy Features

Maria Zoia, Mario Faliva

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In addition, Gram–Charlier-type (GCT) expansions, based on the aforementioned distributions and their orthogonal polynomials, are specified, and an operational criterion is provided to meet modelling requirements in a possibly severe kurtosis and skewness environment. The role played by entropy within the kurtosis ranges of GCT expansions is also examined.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalEntropy
Volume19
DOIs
Publication statusPublished - 2017

Keywords

  • Gram–Charlier-type expansions
  • entropy
  • kurtosis
  • limit laws
  • power-raised hyperbolic secant distributions
  • skewness

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