Many generalised distributions exist for modelling data with vastly diverse characteristics. However, very few of these generalisations of the normal distribution have shape parameters with clear roles that determine, for instance, skewness and tail shape. In this chapter, we review existing skewing mechanisms and their properties in detail. Using the knowledge acquired, we add a skewness parameter to the body-tail generalised normal distribution \cite{BTGN}, that yields the \ac{FIN} with parameters for location, scale, body-shape, skewness, and tail weight. Basic statistical properties of the \ac{FIN} are provided, such as the \ac{PDF}, cumulative distribution function, moments, and likelihood equations. Additionally, the \ac{FIN} \ac{PDF} is extended to a multivariate setting using a student t-copula, yielding the \ac{MFIN}. The \ac{MFIN} is applied to stock returns data, where it outperforms the t-copula multivariate generalised hyperbolic, Azzalini skew-t, hyperbolic, and normal inverse Gaussian distributions.

翻译：许多广义分布可用于对具有极大多样性特征的数据进行建模。然而，在这些正态分布的推广中，极少有分布的形状参数具有明确的作用，例如确定偏度和尾部形状。本章详细回顾了现有的偏度机制及其性质。利用所得知识，我们向体尾广义正态分布\cite{BTGN}中添加一个偏度参数，从而得到了具有位置、尺度、体形状、偏度和尾部权重参数的FIN分布。提供了FIN分布的基本统计性质，如概率密度函数、累积分布函数、矩和似然方程。此外，利用学生t-copula将FIN的概率密度函数推广到多元情形，得到了MFIN分布。将MFIN应用于股票收益率数据，其表现优于t-copula多元广义双曲分布、Azzalini偏t分布、双曲分布和正态逆高斯分布。