We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its L\'evy measure and the tail equivalence between the density and its L\'evy measure density, under monotonic-type assumptions on the L\'evy measure density. The key assumption is that tail of the L\'evy measure density is asymptotic to a non-increasing function or is eventually non-increasing. Our conditions are novel and cover a rather wide class of infinitely divisible distributions. Several significant properties for analyzing the subexponentiality of densities have been derived such as closure properties of [ convolution, convolution roots and asymptotic equivalence ] and the factorization property. Moreover, we illustrate that the results are applicable for developing the statistical inference of subexponential infinitely divisible distributions which are absolutely continuous.
翻译:我们根据L\'evy度量密度的单体型假设,显示了三种特性的等同性:密度的亚爆炸性、其L\'evy度量密度的亚爆炸性、密度和L\'evy度量密度的尾等值。关键假设是L\'evy度量密度的尾部对非增加功能无准备性,或最终没有增加。我们的情况是新奇的,覆盖了相当宽的极不显性分布类别。已经为分析密度的次爆炸性而得出了一些重要的特性,例如[共变、变形根和损等 的封闭性属性和系数化属性。此外,我们说明这些结果适用于开发绝对连续的子爆炸性极多异分布的统计推论。