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

Format:

Book

Author/Creator:

Gzyl, Henryk, 1946- author.

Gomes-Gonçalves, Erika, author.

Mayoral, Silvia, author.

Series:

De Gruyter STEM

Language:

English

Subjects (All):

Loss control--Statistical methods.

Loss control.

Maxium entropy method.

Physical Description:

1 online resource (210 pages) : illustrations

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

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.

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

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 Review of statistical procedures

Index

Bibliography

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110516135

3110516136

OCLC:

1023539563