Loss Data Analysis
：The Maximum Entropy Approach
( De Gruyter Textbook )
Publication subTitle ：The Maximum Entropy Approach
Publication series ： De Gruyter Textbook
Author： Gzyl Henryk;Mayoral Silvia;Gomes-Gonçalves Erika
Publisher： De Gruyter
Publication year： 2018
E-ISBN: 9783110516074
P-ISBN(Paperback): 9783110516043
Subject： O213 applied statistical mathematics
Keyword： 数值分析,概率论（几率论、或然率论）,计算机的应用,数据处理系统及设备,数据处理、数据处理系统,经济计划与管理
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Description
This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences.
On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems.
The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable.
Contents
Introduction
Frequency models
Individual severity models
Some detailed examples
Some traditional approaches to the aggregation problem
Laplace transforms and fractional moment problems
The standard maximum entropy method
Extensions of the method of maximum entropy
Superresolution in maxentropic Laplace transform inversion
Sample data dependence
Disentangling frequencies and decompounding losses
Computations using the maxentropic density
Review of statistical procedures
Chapter