{"title":"Jiandong Ren's Discussion on “Size-Biased Risk Measures of Compound Sums,” by Michel Denuit, January 2020","authors":"Jiandong Ren","doi":"10.1080/10920277.2021.1914666","DOIUrl":null,"url":null,"abstract":"2. SIZE-BIASED TRANSFORM FOR DISTRIBUTIONS IN ða,b, 0Þ CLASS The concept of ða, b, 0Þ class distributions is well known to actuaries, mainly because of the popularity of Panjer’s recursive formulas for calculating the distribution of the corresponding compound sums. For detailed introductions and applications, refer to Klugman, Panjer, and Willmot (2019) and Sundt and Vernic (2009). In this section, we present a result for the sizebiased transform of distributions in the class. For completeness, we begin with two definitions. Definition 1. Let PNðkÞ denote the probability function of a discrete random variable N; it is a member of the ða, b, 0Þ class of distributions if there exist constants a and b such that","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1914666","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10920277.2021.1914666","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
2. SIZE-BIASED TRANSFORM FOR DISTRIBUTIONS IN ða,b, 0Þ CLASS The concept of ða, b, 0Þ class distributions is well known to actuaries, mainly because of the popularity of Panjer’s recursive formulas for calculating the distribution of the corresponding compound sums. For detailed introductions and applications, refer to Klugman, Panjer, and Willmot (2019) and Sundt and Vernic (2009). In this section, we present a result for the sizebiased transform of distributions in the class. For completeness, we begin with two definitions. Definition 1. Let PNðkÞ denote the probability function of a discrete random variable N; it is a member of the ða, b, 0Þ class of distributions if there exist constants a and b such that
2. 关于ða,b, 0Þ类类分布的概念对于精算师来说是非常熟悉的，这主要是因为Panjer的递归公式在计算相应的复和分布时非常流行。有关详细的介绍和应用，请参见Klugman, Panjer, and Willmot(2019)和Sundt and Vernic(2009)。在本节中，我们给出了类中分布的大小偏置变换的结果。为了完整起见，我们从两个定义开始。定义1。设PNðkÞ表示离散随机变量N的概率函数;如果存在常数a和b，则它是分布类的一个成员
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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