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Loss Data Analysis

The Maximum Entropy Approach

Authors: Henryk Gzyl, Silvia Mayoral, Erika Gomes-Gonçalves Publisher: De Gruyter Publication date: 2018 Publication language: Angielski Number of pages: 210 Publication formats: EAN: 9783110516074 ISBN: 9783110516074 Category: Economic statistics Numerical analysis Probability & statistics Databases Publisher's index: - Bibliographic note: -

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

TOC

  • Preface 8
  • Contents 10
  • 1 Introduction 14
  • 2 Frequency models 18
  • 3 Individual severity models 36
  • 4 Some detailed examples 44
  • 5 Some traditional approaches to the aggregation problem 52
  • 6 Laplace transforms and fractional moment problems 76
  • 7 The standard maximum entropy method 90
  • 8 Extensions of the method of maximum entropy 112
  • 9 Superresolution in maxentropic Laplace transform inversion 128
  • 10 Sample data dependence 134
  • 11 Disentangling frequencies and decompounding losses 152
  • 12 Computations using the maxentropic density 168
  • 13 Review of statistical procedures 178
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