Some properties of skew-symmetric distributions

Article

DOI: 10.1007/s10463-011-0338-5

Cite this article as:
Azzalini, A. & Regoli, G. Ann Inst Stat Math (2012) 64: 857. doi:10.1007/s10463-011-0338-5

Abstract

The family of skew-symmetric distributions is a wide set of probability density functions obtained by suitably combining a few components which can be quite freely selected provided some simple requirements are satisfied. Although intense recent work has produced several results for certain sub-families of this construction, much less is known in general terms. The present paper explores some questions within this framework and provides conditions for the above-mentioned components to ensure that the final distribution enjoys specific properties.

Keywords

Central symmetry Log-concavity Peakedness Quasi-concavity Skew-symmetric distributions Stochastic ordering Strong unimodality Unimodality 

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2011

Authors and Affiliations

  1. 1.Dipartimento di Scienze StatisticheUniversità di PadovaPaduaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di PerugiaPerugiaItaly