Statistical Methods for Fuzzy Data
(Sprache: Englisch)
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics...
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Produktinformationen zu „Statistical Methods for Fuzzy Data “
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively.
Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information.
Key Features:
* Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data.
* Describes methods of increasing importance with applications in areas such as environmental statistics and social science.
* Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples.
* Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data.
This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
Klappentext zu „Statistical Methods for Fuzzy Data “
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively.Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information.
Key Features:
* Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data.
* Describes methods of increasing importance with applications in areas such as environmental statistics and social science.
* Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples.
* Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data.
This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
Inhaltsverzeichnis zu „Statistical Methods for Fuzzy Data “
Preface.Part I FUZZY INFORMATION.
1. Fuzzy Data.
1.1 One-dimensional Fuzzy Data.
1.2 Vector-valued Fuzzy Data.
1.3 Fuzziness and Variability.
1.4 Fuzziness and Errors.
1.5 Problems.
2. Fuzzy Numbers and Fuzzy Vectors.
2.1 Fuzzy Numbers and Characterizing Functions.
2.2 Vectors of Fuzzy Numbers and Fuzzy Vectors.
2.3 Triangular Norms.
2.4 Problems.
3. Mathematical Operations for Fuzzy Quantities.
3.1 Functions of Fuzzy Variables.
3.2 Addition of Fuzzy Numbers.
3.3 Multiplication of Fuzzy Numbers.
3.4 Mean Value of Fuzzy Numbers.
3.5 Differences and Quotients.
3.6 Fuzzy Valued Functions.
3.7 Problems.
Part II DESCRIPTIVE STATISTICS FOR FUZZY DATA.
4. Fuzzy Samples.
4.1 Minimum of Fuzzy Data.
4.2 Maximum of Fuzzy Data.
4.3 Cumulative Sum for Fuzzy Data.
4.4 Problems.
5. Histograms for Fuzzy Data.
5.1 Fuzzy Frequency of a Fixed Class.
5.2 Fuzzy Frequency Distributions.
5.3 Axonometric Diagram of the Fuzzy Histogram.
5.4 Problems.
6. Empirical Distribution Functions.
6.1 Fuzzy Valued Empirical Distribution Function.
6.2 Fuzzy Empirical Fractiles.
6.3 Smoothed Empirical Distribution Function.
6.4 Problems.
7. Empirical Correlation for Fuzzy Data.
7.1 Fuzzy Empirical Correlation Coefficient.
7.2 Problems.
Part III FOUNDATIONS OF STATISTICAL INFERENCE WITH FUZZY DATA.
8. Fuzzy Probability Distributions.
8.1 Fuzzy Probability Densities.
8.2 Probabilities based on Fuzzy Probability Densities.
8.3 General Fuzzy Probability Distributions.
8.4 Problems.
9. A Law of Large Numbers.
9.1 Fuzzy Random Variables.
9.2 Fuzzy Probability Distributions induced by
... mehr
Fuzzy Random Variables.
9.3 Sequences of Fuzzy Random Variables.
9.4 Law of Large Numbers for Fuzzy Random Variables.
9.5 Problems.
10. Combined Fuzzy Samples.
10.1 Observation Space and Sample Space.
10.2 Combination of Fuzzy Samples.
10.3 Statistics of Fuzzy Data.
10.4 Problems.
Part IV CLASSICAL STATISTICAL INFERENCE FOR FUZZY DATA.
11. Generalized Point Estimations.
11.1 Estimations based on Fuzzy Samples.
11.2 Sample Moments.
11.3 Problems.
12. Generalized Confidence Regions.
12.1 Confidence Functions.
12.2 Fuzzy Confidence Regions.
12.3 Problems.
13. Statistical Tests for Fuzzy Data.
13.1 Test Statistics and Fuzzy Data.
13.2 Fuzzy p-Values.
13.3 Problems.
Part V BAYESIAN INFERENCE AND FUZZY INFORMATION.
14. Bayes' Theorem and Fuzzy Information.
14.1 Fuzzy a-priori Distributions.
14.2 Updating Fuzzy a-priori Distributions.
14.3 Problems.
15. Generalized Bayes' Theorem.
15.1 Likelihood Function for Fuzzy Data.
15.2 Bayes' Theorem for Fuzzy a-priori Distribution and Fuzzy Data.
15.3 Problems.
16. Bayesian Confidence Regions.
16.1 Confidence Regions based on Fuzzy Data.
16.2 Fuzzy HPD-Regions.
16.3 Problems.
17. Fuzzy Predictive Distributions.
17.1 Discrete Case.
17.2 Discrete Models with Continuous Parameter Space.
17.3 Continuous Case.
17.4 Problems.
18. Bayesian
9.3 Sequences of Fuzzy Random Variables.
9.4 Law of Large Numbers for Fuzzy Random Variables.
9.5 Problems.
10. Combined Fuzzy Samples.
10.1 Observation Space and Sample Space.
10.2 Combination of Fuzzy Samples.
10.3 Statistics of Fuzzy Data.
10.4 Problems.
Part IV CLASSICAL STATISTICAL INFERENCE FOR FUZZY DATA.
11. Generalized Point Estimations.
11.1 Estimations based on Fuzzy Samples.
11.2 Sample Moments.
11.3 Problems.
12. Generalized Confidence Regions.
12.1 Confidence Functions.
12.2 Fuzzy Confidence Regions.
12.3 Problems.
13. Statistical Tests for Fuzzy Data.
13.1 Test Statistics and Fuzzy Data.
13.2 Fuzzy p-Values.
13.3 Problems.
Part V BAYESIAN INFERENCE AND FUZZY INFORMATION.
14. Bayes' Theorem and Fuzzy Information.
14.1 Fuzzy a-priori Distributions.
14.2 Updating Fuzzy a-priori Distributions.
14.3 Problems.
15. Generalized Bayes' Theorem.
15.1 Likelihood Function for Fuzzy Data.
15.2 Bayes' Theorem for Fuzzy a-priori Distribution and Fuzzy Data.
15.3 Problems.
16. Bayesian Confidence Regions.
16.1 Confidence Regions based on Fuzzy Data.
16.2 Fuzzy HPD-Regions.
16.3 Problems.
17. Fuzzy Predictive Distributions.
17.1 Discrete Case.
17.2 Discrete Models with Continuous Parameter Space.
17.3 Continuous Case.
17.4 Problems.
18. Bayesian
... weniger
Bibliographische Angaben
- Autor: Reinhard Viertl
- 2011, 1. Auflage, 256 Seiten, Maße: 15,5 x 23,4 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470699450
- ISBN-13: 9780470699454
Sprache:
Englisch
Rezension zu „Statistical Methods for Fuzzy Data “
"I recommend this book to anyone interested in exploring new approaches to the extraction of information from novel data sources." ( International Statistical Review , 2012)
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