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Fuzzy Statistical Inferences Based on Fuzzy Random Variables [Kõva köide]

(Payame Noor University (Shahrekourd), Iran)
  • Formaat: Hardback, 288 pages, kõrgus x laius: 234x156 mm, kaal: 562 g, 100 Tables, black and white; 24 Line drawings, black and white; 24 Illustrations, black and white
  • Ilmumisaeg: 25-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032162228
  • ISBN-13: 9781032162225
Teised raamatud teemal:
Fuzzy Statistical Inferences Based on Fuzzy Random VariablesSuurem pilt
  • Formaat: Hardback, 288 pages, kõrgus x laius: 234x156 mm, kaal: 562 g, 100 Tables, black and white; 24 Line drawings, black and white; 24 Illustrations, black and white
  • Ilmumisaeg: 25-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032162228
  • ISBN-13: 9781032162225
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032162225.html
Märksõnad:
This book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text on fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models. The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required.

Key Features:





Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data.

The book is suitable for students and researchers in statistics, social science, engineering, and economics, and it can be used at graduate and P.h.D level.

Arvustused

"This book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text of fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models. The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required." - MathSciNet

Foreword xi
Preface xiii
List of Figures
xv
List of Tables
xvii
Symbols xxi
I Fuzzy Statistical Inferences Based on Fuzzy Random Variables
1(262)
1 Introduction
3(38)
1.1 Fuzzy Set
3(10)
1.1.1 Operations of fuzzy sets
6(6)
1.1.2 Cartesian product of fuzzy sets
12(1)
1.2 Fuzzy Numbers
13(12)
1.2.1 A similarity measure
16(2)
1.2.2 A criteria for ranking FNs
18(4)
1.2.3 Distance measure
22(3)
1.3 a-values of FNs
25(12)
1.3.1 A generalized difference for FNs
31(3)
1.3.2 Maximum and minimum of the two FNs
34(2)
1.3.3 Absolute value of a FN
36(1)
1.4 Exercise
37(2)
1.5 Glossary
39(2)
2 Probability of a Fuzzy Event
41(32)
2.1 Non-fuzzy Probability of a Fuzzy Event
42(7)
2.2 Probability of a Fuzzy Product Event
49(3)
2.3 Conditional Probability, Independence, and Bayes' Theorem
52(3)
2.4 Fuzzy Probability of a FE and Its Properties
55(12)
2.5 Exercise
67(4)
2.6 Glossary
71(2)
3 Descriptive Statistics Based on Fuzzy Data
73(24)
3.1 Central Tendency
73(4)
3.2 Fuzzy Deviation Criteria
77(4)
3.3 Box Plot Based on Fuzzy Data
81(3)
3.4 Descriptive Statistics Based on Grouped Fuzzy Data
84(6)
3.5 Measure of Spread Based on Fuzzy Data
90(4)
3.6 Exercise
94(2)
3.7 Glossary
96(1)
4 Probability Reasoning Based on Fuzzy Random Variable (FRV)
97(40)
4.1 Fuzzy Random Variables
97(26)
4.1.1 Fuzzy expectation and exact variance
99(3)
4.1.2 Correlation between two FRVs
102(3)
4.1.3 Probability of an interval based on FRVs
105(2)
4.1.4 Liminf and limsup for a sequence of FRVs
107(1)
4.1.5 Fuzzy cumulative distribution function
108(5)
4.1.6 Location-Scale FRVs
113(10)
4.2 Probabilistic Inequalities for Fuzzy Random Variables
123(3)
4.3 Limit Theorems Based on FRVs
126(8)
4.4 Exercise
134(2)
4.5 Glossary
136(1)
5 Fuzzy Hypothesis Testing for FRVs
137(56)
5.1 Testing Fuzzy Hypotheses Based on Normal FRVs
138(17)
5.1.1 One-sample testing fuzzy hypotheses based on normal FRVs
140(8)
5.1.2 Two-samples testing fuzzy hypotheses based on normal FRVs
148(7)
5.2 Statistical Non-parametric Tests Based on FRVs
155(23)
5.2.1 Sign test
155(4)
5.2.2 Wilcoxon test
159(3)
5.2.3 Kolmogorov-Smirnov test based on FRVs
162(1)
5.2.3.1 One-sample Kolmogorov-Smirnov test
162(4)
5.2.3.2 Two-sample Kolmogorov-Smirnov test for TFRVs
166(4)
5.2.4 Kruskal-Wallis test
170(8)
5.3 One-Way ANOVA Based on FRVs
178(5)
5.4 Exercise
183(7)
5.5 Glossary
190(3)
6 Fuzzy Quality Control and Reliability Systems for FRVs
193(34)
6.1 Fuzzy Control Charts and Capability Indices Based on NFRVs
193(17)
6.1.1 Fuzzy 5-chart and s-chart for NFRVs
194(3)
6.1.2 Fuzzy EWMA chart based on NFRVs
197(5)
6.1.3 Process capability indices based on NFRVs
202(7)
6.1.4 Testing hypotheses for fuzzy process capability Cp
209(1)
6.2 Reliability Evaluation Using FRVs
210(10)
6.2.1 Components of a reliability system based on LTFRVs
212(8)
6.3 Exercise
220(6)
6.4 Glossary
226(1)
7 Regression and Time Series Models for FRVs
227(36)
7.1 Regression Analysis Based on FRVs
227(14)
7.1.1 A multivariate regression analysis based on FRVs
228(7)
7.1.2 Fuzzy non-parametric regression model
235(6)
7.2 Time Series Models for FRVs
241(16)
7.2.1 Autocorrelation criterion based on a fuzzy time series
242(4)
7.2.2 Multivariate time series model based on fuzzy time series data
246(7)
7.2.3 Non-parametric time series model based on fuzzy time series data
253(4)
7.3 Exercise
257(4)
7.4 Glossary
261(2)
Bibliography 263(16)
Index 279
Gholamreza Hesamian is associate professor of Statistics at Payame Noor University, Iran. His research areas include decision theory, probability theory, fuzzy mathematics and statistics.