Description

Book Synopsis

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

Loss Data Analysis: The Maximum Entropy Approach

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    A Paperback by Henryk Gzyl, Silvia Mayoral, Erika Gomes-Gonçalves

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      Book details

      Publisher De Gruyter
      Published 6 March 2023
      ISBN-13 9783111047386
      978-3111047386
      ISBN-10 3111047385
      Also in:
      Data capture and analysis Applied mathematics Probability and statistics

      Description

      Book Synopsis

      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

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