Loss Data Analysis : : The Maximum Entropy Approach / / Henryk Gzyl, Silvia Mayoral, Erika Gomes-Gonçalves.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1
• VerfasserIn: Gzyl, Henryk,; Gomes-Gonçalves, Erika,; Mayoral, Silvia,
• MitwirkendeR: Gomes-Gonçalves, Erika,; Gzyl, Henryk,; Mayoral, Silvia,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; ©2023
• Year of Publication: 2023
• Edition: 2nd extended edition
• Language: English
• Series: De Gruyter STEM
• Physical Description: 1 online resource (XII, 210 p.)

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. ContentsIntroductionFrequency modelsIndividual severity modelsSome detailed examplesSome traditional approaches to the aggregation problemLaplace transforms and fractional moment problemsThe standard maximum entropy methodExtensions of the method of maximum entropySuperresolution in maxentropic Laplace transform inversionSample data dependenceDisentangling frequencies and decompounding lossesComputations using the maxentropic densityReview of statistical procedures

Table of Contents

Frontmatter -- Preface -- Contents -- 1 Introduction -- 2 Frequency models -- 3 Individual severity models -- 4 Some detailed examples -- 5 Some traditional approaches to the aggregation problem -- 6 Laplace transforms and fractional moment problems -- 7 The standard maximum entropy method -- 8 Extensions of the method of maximum entropy -- 9 Superresolution in maxentropic Laplace transform inversion -- 10 Sample data dependence -- 11 Disentangling frequencies and decompounding losses -- 12 Computations using the maxentropic density -- 13 A solution to the capital allocation problem -- 14 Review of statistical procedures -- Bibliography -- Index