Further Results on a Class of Distributions which Includes the Normal Ones – Looking Back
Keywords:Skew-symmetric distributions, Subbotin distribution, Symmetry-modulated distributions
The author’s 1986 paper with the same title is reprinted here alongside some comments and corrections. The original abstract, here translated in English, was as follows: "Some further results are presented concerning a class of density functions already examined in another work of the author (1985). Specifically, an additional shape parameter is introduced which allows a wide range of the coefficients of asymmetry and kurtosis."
J. ANDEL, I. NETUKA, K. ZVÁRA (1984). On threshold autoregressive processes. Kibernetika, 20, pp. 89–106.
A. AZZALINI, A. CAPITANIO (1999). Statistical applications of the multivariate skew normal distribution. Journal of the Royal Statistical Society, series B, 61, no. 3, pp. 579–602. Full version of the paper at arXiv.org:0911.2093.
A. AZZALINI, A. CAPITANIO (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, series B, 65, no. 2, pp. 367–389. Full version of the paper at arXiv.org:0911.2342.
A. AZZALINI, A. DALLA VALLE (1996). The multivariate skew-normal distribution. Biometrika, 83, pp. 715–726.
A. AZZALINI, M. G. GENTON (2008). Robust likelihood methods based on the skew-t and related distributions. International Statistical Review, 76, pp. 106–129.
N. HENZE (1986). A probabilistic representation of the 'skew-normal' distribution. Scandinavian Journal of Statistics, 13, pp. 271–275.
M. T. SUBBOTIN (1923). On the law of frequency of error. Matematicheskii Sbornik, 31, pp. 296–301.
J.WANG, J. BOYER, M. G. GENTON (2004). A skew-symmetric representation of multivariate distributions. Statistica Sinica, 14, pp. 1259–1270.