论文标题
从帕累托到威布尔 - $ \ mathbb {r}^+$上的分布的建设性评论
From Pareto to Weibull -- a constructive review of distributions on $\mathbb{R}^+$
论文作者
论文摘要
具有指数截止的权力法律和权力法是在积极的一半线上的两个不同的分布家族。在本文中，我们通过建立一个分布家族来对两个家庭提出统一的处理，这些分布家族在它们之间插入，我们称之为插值家庭（如果）分布。我们的原始结构依赖于统计物理学的技术，它为迄今无关分布（如帕累托和威布尔分布）提供了联系，并为它们提供了新的灯光。 IF还包含几个分布，这些分布既不是权力法，也不包含具有指数截止类型的权力法。我们为IF计算基于分位数的属性，时刻和模式。这使我们能够在$ \ mathbb {r}^+$上查看已知分布的已知属性，并为我们的插值家庭的各种鲜为人知（和新的）特殊案例提供单一扫描这些特征。
Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, which we call Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of power law nor of power law with exponential cut-off type. We calculate quantile-based properties, moments and modes for the IF. This allows us to review known properties of famous distributions on $\mathbb{R}^+$ and to provide in a single sweep these characteristics for various less known (and new) special cases of our Interpolating Family.
