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 b...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Chichester, West Sussex :
Wiley
2011.
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| Edición: | 1st edition |
| Colección: | Wiley Series in Probability and Statistics
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628985706719 |
Tabla de Contenidos:
- Statistical Methods forFuzzy Data; Contents; 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 quotients3.6 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 data7.1 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 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 samples10.1 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 estimators; 11.1 Estimators 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 information14.1 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 Bayesian 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 decisions and fuzzy information
