Tail dependence of generalized modified skew slash distribution
In the last decades, slash distributions have received broad attention; \textit{W. H. Rogers} and \textit{J. W. Tukey} [Stat. Neerl. 26, No. 3, 211--226 (1972; Zbl 0245.62021)] introduced the slash distribution for data analysis. \textit{O. Arslan} and \textit{A. İ. Genç} [J. Stat. Plann. Inference 139, No. 3, 1164--1170 (2009; Zbl 1157.60304)] studied the multivariate slash distribution. \textit{H. W. Gómez} et al. [Stat. Probab. Lett. 77, No. 7, 717--725 (2007; Zbl 1116.62015)] extended the slash distribution to the slash elliptical family, \textit{A. İ. Genç} [Commun. Stat., Simulation Comput. 36, No. 5, 937--947 (2007; Zbl 1126.62006)] proposed an asymmetric generalization of the slash distribution, and \textit{J. Reyes} et al. [Symmetry 10, No. 12, Paper No. 724, 18 p. (2018; Zbl 1426.60015)] discussed the generalized modified slash (GMS) distribution, where the uniform distribution was replaced by the gamma distribution. In this work, the authors introduce a generalized modified skew slash distribution. Some of its basic properties are obtained. In addition, the tail dependence coefficients of the bivariate generalized modified skew slash distribution are derived and some special cases are discussed. More precisely, they look the generalized modified skew slash (GMSS) distribution, which has the following stochastic representation \[ Y:=\mu+\sigma(W/V), \] where \(W\sim SN(0;1;\lambda)\) and \(V\sim Ga(2\beta;\beta)\) are independent, \(\mu\in \mathbb{R}\) is the location parameter, \(\sigma>0\) is the scale parameter, \(\lambda\in \mathbb{R}\) is the skew parameter, and \(\beta>0\) is the parameter related to the distribution's kurtosis, and denoted by \(Y\sim GMSS(\mu;\sigma^2;\lambda;\beta)\). Furthermore, the multivariate generalized modified skew slash (MGMSS) distribution is discussed and the tail dependence coefficients of bivariate GMSS distribution are derived at the end of the paper.
generalized modified skew slash distribution
scientific article; zbMATH DE number 7471943