Loss Data Analysis :: the Maximum Entropy Approach.
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 reliabili...
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| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin/Boston :
De Gruyter, Inc.,
2018.
|
| Series: | De Gruyter Textbook Ser.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| 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. 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. |
| Physical Description: | 1 online resource (210 pages) |
| ISBN: | 3110516071 9783110516074 |
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| 505 | 0 | |a Intro; 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. | |
| 520 | |a 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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| contents | Intro; 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. |
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| id | ZDB-4-EBA-on1023539563 |
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| indexdate | 2025-04-11T08:44:08Z |
| institution | BVB |
| isbn | 3110516071 9783110516074 |
| language | English |
| oclc_num | 1023539563 |
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| spelling | Gzyl, Henryk. Loss Data Analysis : the Maximum Entropy Approach. Berlin/Boston : De Gruyter, Inc., 2018. 1 online resource (210 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Textbook Ser. Print version record. Intro; 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. 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 control Statistical methods. Maxium entropy method. Contrôle des pertes Méthodes statistiques. MATHEMATICS Probability & Statistics General. bisacsh Electronic books. Mayoral, Silvia. Gomes-Goncalves, Erika. has work: Loss data analysis (Text) https://id.oclc.org/worldcat/entity/E39PCGTqyWdQbxy8J3mJmKVtJC https://id.oclc.org/worldcat/ontology/hasWork Print version: Gzyl, Henryk. Loss Data Analysis : The Maximum Entropy Approach. Berlin/Boston : De Gruyter, Inc., ©2018 9783110516043 |
| spellingShingle | Gzyl, Henryk Loss Data Analysis : the Maximum Entropy Approach. De Gruyter Textbook Ser. Intro; 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. Loss control Statistical methods. Maxium entropy method. Contrôle des pertes Méthodes statistiques. MATHEMATICS Probability & Statistics General. bisacsh |
| title | Loss Data Analysis : the Maximum Entropy Approach. |
| title_auth | Loss Data Analysis : the Maximum Entropy Approach. |
| title_exact_search | Loss Data Analysis : the Maximum Entropy Approach. |
| title_full | Loss Data Analysis : the Maximum Entropy Approach. |
| title_fullStr | Loss Data Analysis : the Maximum Entropy Approach. |
| title_full_unstemmed | Loss Data Analysis : the Maximum Entropy Approach. |
| title_short | Loss Data Analysis : |
| title_sort | loss data analysis the maximum entropy approach |
| title_sub | the Maximum Entropy Approach. |
| topic | Loss control Statistical methods. Maxium entropy method. Contrôle des pertes Méthodes statistiques. MATHEMATICS Probability & Statistics General. bisacsh |
| topic_facet | Loss control Statistical methods. Maxium entropy method. Contrôle des pertes Méthodes statistiques. MATHEMATICS Probability & Statistics General. Electronic books. |
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