Information-theoretic methods for estimating complicated probability distributions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2006
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Mathematics in science and engineering
v. 207 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Includes bibliographical references (p. 289-293) and index Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC. |
| Beschreibung: | 1 Online-Ressource (xvii, 299 p.) |
| ISBN: | 9780444527967 0444527966 9780080463704 0080463703 0080463851 |
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| 500 | |a In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. | ||
| 500 | |a There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. | ||
| 500 | |a It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC. | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Zong, Zhi |
| author_facet | Zong, Zhi |
| author_role | aut |
| author_sort | Zong, Zhi |
| author_variant | z z zz |
| building | Verbundindex |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/4 |
| dewey-search | 519.2/4 |
| dewey-sort | 3519.2 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:18:16Z |
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| isbn | 9780444527967 0444527966 9780080463704 0080463703 0080463851 |
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| series2 | Mathematics in science and engineering |
| spelling | Zong, Zhi Verfasser aut Information-theoretic methods for estimating complicated probability distributions Zhi Zong 1st ed Amsterdam Elsevier 2006 1 Online-Ressource (xvii, 299 p.) txt rdacontent c rdamedia cr rdacarrier Mathematics in science and engineering v. 207 Includes bibliographical references (p. 289-293) and index Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC. MATHEMATICS / Probability & Statistics / General bisacsh Approximation theory fast Distribution (Probability theory) fast Information theory fast Distribution (Probability theory) Information theory Approximation theory Festbett (DE-588)4113548-9 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Festbettreaktor (DE-588)4113549-0 gnd rswk-swf Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Chemischer Reaktor (DE-588)4121085-2 gnd rswk-swf Informationstheoretisches Modell (DE-588)4161675-3 gnd rswk-swf Füllkörpersäule (DE-588)4155581-8 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Informationstheorie (DE-588)4026927-9 s Spline-Approximation (DE-588)4182394-1 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s 1\p DE-604 Schätzung (DE-588)4193791-0 s Informationstheoretisches Modell (DE-588)4161675-3 s 2\p DE-604 Chemischer Reaktor (DE-588)4121085-2 s Festbettreaktor (DE-588)4113549-0 s DE-604 Festbett (DE-588)4113548-9 s Füllkörpersäule (DE-588)4155581-8 s http://www.sciencedirect.com/science/book/9780444527967 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zong, Zhi Information-theoretic methods for estimating complicated probability distributions MATHEMATICS / Probability & Statistics / General bisacsh Approximation theory fast Distribution (Probability theory) fast Information theory fast Distribution (Probability theory) Information theory Approximation theory Festbett (DE-588)4113548-9 gnd Schätzung (DE-588)4193791-0 gnd Informationstheorie (DE-588)4026927-9 gnd Festbettreaktor (DE-588)4113549-0 gnd Spline-Approximation (DE-588)4182394-1 gnd Chemischer Reaktor (DE-588)4121085-2 gnd Informationstheoretisches Modell (DE-588)4161675-3 gnd Füllkörpersäule (DE-588)4155581-8 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4113548-9 (DE-588)4193791-0 (DE-588)4026927-9 (DE-588)4113549-0 (DE-588)4182394-1 (DE-588)4121085-2 (DE-588)4161675-3 (DE-588)4155581-8 (DE-588)4121894-2 |
| title | Information-theoretic methods for estimating complicated probability distributions |
| title_auth | Information-theoretic methods for estimating complicated probability distributions |
| title_exact_search | Information-theoretic methods for estimating complicated probability distributions |
| title_full | Information-theoretic methods for estimating complicated probability distributions Zhi Zong |
| title_fullStr | Information-theoretic methods for estimating complicated probability distributions Zhi Zong |
| title_full_unstemmed | Information-theoretic methods for estimating complicated probability distributions Zhi Zong |
| title_short | Information-theoretic methods for estimating complicated probability distributions |
| title_sort | information theoretic methods for estimating complicated probability distributions |
| topic | MATHEMATICS / Probability & Statistics / General bisacsh Approximation theory fast Distribution (Probability theory) fast Information theory fast Distribution (Probability theory) Information theory Approximation theory Festbett (DE-588)4113548-9 gnd Schätzung (DE-588)4193791-0 gnd Informationstheorie (DE-588)4026927-9 gnd Festbettreaktor (DE-588)4113549-0 gnd Spline-Approximation (DE-588)4182394-1 gnd Chemischer Reaktor (DE-588)4121085-2 gnd Informationstheoretisches Modell (DE-588)4161675-3 gnd Füllkörpersäule (DE-588)4155581-8 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Approximation theory Distribution (Probability theory) Information theory Festbett Schätzung Informationstheorie Festbettreaktor Spline-Approximation Chemischer Reaktor Informationstheoretisches Modell Füllkörpersäule Wahrscheinlichkeitsverteilung |
| url | http://www.sciencedirect.com/science/book/9780444527967 |
| work_keys_str_mv | AT zongzhi informationtheoreticmethodsforestimatingcomplicatedprobabilitydistributions |