主 题: 第28期学术午餐会活动——Signed- and Quasi-infinitely Divisible Distributions on Non-negative Integers: with Relation to Negative Probabilities
报告人: 张慧铭 2016级普博 (北京大学)
时 间: 2017-12-07 12:00-13:30
地 点: Room 1418, Sciences Building No. 1
各位数院研究生同学：
研究生学术午餐会是在学院领导的大力支持下，由研究生会负责组织的系列学术交流活动。午餐会每次邀请一位同学作为主讲人，面向全院各专业背景的研究生介绍自己科研方向的基本问题、概念和方法，并汇报近期的研究成果和进展，是研究生展示自我、促进交流的学术平台，已经举办了二十七期活动。研究生会将于2017年12月7日周四举办第28期学术午餐会活动，欢迎感兴趣的老师和同学积极报名参加。
报告人简介：张慧铭，2016级普博，导师有多位，分别是贾金柱、姚方和陈松蹊教授，目前的研究兴趣有：高维统计、高维概率论、无穷可分分布与莱维过程、广义线性模型、函数型数据分析。
报告摘要：In this talk, at first, we give a "half-coins" example concerning negative probabilities model and quasi-infinite divisibility (ID) proposed by Prof. Szekely, G. J.. We next extend Feller's characterization of discrete ID distributions to signed discrete ID distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the Wiener–Lévy theorem in Fourier analysis. This characterization is a special case of an open problem: "Find a necessary and sufficient condition for the Lévy-Khinchine representation with signed Lévy measure to hold", which is proposed by Sato(2014), Chaumont and Yor(2012). We show that many distributions are DPCP by the non-zero p.g.f. property, such as the mixed Poisson distribution and fractional Poisson process. Introduced by Bent Jorgensen (1987, J. Roy. Statist. Soc. B), the Jorgensen set (the set such that the positive real power of the characteristic function maintains as a characteristic function) is a tool to study the exponential dispersion models which is a generalization of the generalized linear models. The Jorgensen set is a semigroup containing 1. DPCP has some bizarre properties, and one is that the parameter λ in the DPCP class cannot be arbitrarily small, this property is related to a research problem in theoretical probability: "Find the Jorgensen set of quasi ID characteristic function". As an application, by a property that a nonnegative integer-valued r.v. X with P(X=0)>0.5 is DPCP, we give an algorithm to fit any count data via adding dummy frequencies.
报名方式：请有意参加的老师在2017年12月6日（周三）中午11点前发送邮件至smsxueshu@126.com，我们将回复邮件和您确认，邮件报名方式仅限于老师，有意参加的同学请点击报名链接https://www.wjx.top/jq/18800832.aspx，谢谢~
