Statistical methods for fuzzy data / Reinhard Viertl.

Format:

Book

Author/Creator:

Viertl, R. (Reinhard)

Series:

Wiley Series in Probability and Statistics

Language:

English

Subjects (All):

Fuzzy measure theory.

Fuzzy sets.

Mathematical statistics.

Physical Description:

1 online resource (270 p.)

Edition:

1st edition

Place of Publication:

Chichester, West Sussex : Wiley, 2011.

Language Note:

English

System Details:

text file

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613678317

9781280767548

1280767545

9780470974421

0470974427

9780470974414

0470974419

OCLC:

701311244