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. 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 测量的单体型假设,显示了三种特性的等同性:密度的亚值、L\'evy测量的密度的亚值以及密度和L\'evy测量密度的尾等值。关键假设是,L\'evy测量密度的尾部对非增加功能没有作用,或者最终没有增加。我们的情况是新奇的,覆盖了相当宽的极易变分布类别。为分析密度的次值所得出的若干重要特性,例如[共变、相变根和等 的封闭属性和系数化属性。此外,我们说明,结果适用于开发绝对连续的子爆炸性极分异分布的统计推论。