The Beta-Hyperbolic Secant Distribution

Austrian Journal of Statistics

article

Matthias J. Fischer¹  David Vaughan² 

[1] University of Erlangen-Nürnberg;Wilfrid Laurier University

关键词: Skewness;    Kurtosis;    Beta-logistic Distribution;    Beta distribution;    Weighting Function;    Glass Fibre Data;    Aluminium Returns.;   

DOI  :  10.17713/ajs.v39i3.247

学科分类：医学（综合）

来源: Austrian Statistical Society

【 摘 要 】

The shape of a probability distribution is often summarized by the distribution’s skewness and kurtosis. Starting from a symmetric “parent” density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every density w on the interval (0; 1) is a specific weighting function. Within this work, we follow up a proposal of Jones (2004) and choose the Beta distribution asunderlying weighting function w. “Parent” distributions like the Student-t, the logistic and the normal distribution have already been investigated in the literature. Based on the assumption that f is the density of a hyperbolic secant distribution, we introduce the Beta-hyperbolic secant (BHS) distribution. In contrast to the Beta-normal distribution and to the Beta-Student-t distribution, BHS densities are always unimodal and all moments exist. In contrast to the Beta-logistic distribution, the BHS distribution is more flexibleregarding the range of skewness and leptokurtosis combinations. Moreover,we propose a generalization which nests both the Beta-logistic and the BHS distribution. Finally, the goodness-of-fit between all above-mentioned distributions is compared for glass fibre data and aluminium returns.

【 授权许可】

CC BY