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E-grāmata: Decision Processes by Using Bivariate Normal Quantile Pairs

  • Formāts: PDF+DRM
  • Izdošanas datums: 07-Oct-2015
  • Izdevniecība: Springer, India, Private Ltd
  • Valoda: eng
  • ISBN-13: 9788132223641
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  • Formāts: PDF+DRM
  • Izdošanas datums: 07-Oct-2015
  • Izdevniecība: Springer, India, Private Ltd
  • Valoda: eng
  • ISBN-13: 9788132223641
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This book discusses equi-quantile values and their use in generating decision alternatives under the twofold complexities of uncertainty and dependence, offering scope for surrogating between two alternative portfolios when they are correlated. The book begins with a discussion on components of rationality and learning models as indispensable concepts in decision-making processes. It identifies three-fold complexities in such processes: uncertainty, dependence and dynamism.

The book is a novel attempt to seek tangible solutions for such decision problems. To do so, four hundred tables of bi-quantile pairs are presented for carefully chosen grids. In fact, it is a two-variable generalization of the inverse normal integral table, which is used in obtaining bivariate normal quantile pairs for the given values of probability and correlation. When making decisions, only two of them have to be taken at a time. These tables are essential tools for decision-making under risk and dependence, and offer scope for delving up to a single step of dynamism. The book subsequently addresses averments dealing with applications and advantages.

The content is useful to empirical scientists and risk-oriented decision makers who are often required to make choices on the basis of pairs of variables. The book also helps simulators seeking valid confidence intervals for their estimates, and particle physicists looking for condensed confidence intervals for HiggsBoson utilizing the BoseEinstein correlation given the magnitude of such correlations. Entrepreneurs and investors as well as students of management, statistics, economics and econometrics, psychology, psychometrics and psychographics, social sciences, geographic information system, geology, agricultural and veterinary sciences, medical sciences and diagnostics, and remote sensing will also find the book very useful.

    
1 Introduction
1(18)
1.1 Decision-Making
1(1)
1.2 Components of Rationality and Learning Model
2(2)
1.3 Predicate (Stochastic) Calculus for Psycho-Kinetics of Personality Development
4(6)
1.4 Truth and Error
10(2)
1.5 The Main Users
12(1)
1.6
Chapter Plan
13(6)
References
17(2)
2 Decision Complexity and Methods to Meet Them
19(28)
2.1 Decision Complexities: Triangular Structure
19(2)
2.2 Vertex of Uncertainty (V1): Evidence of Probabilistic Thought During the Vedic and the Post-Vedic Period
21(2)
2.3 Probability and Its Measure as Discovered in European Continent
23(1)
2.4 Probability Distribution
24(1)
2.5 Probability Updating
25(1)
2.6 The Vertex of Dependence (V2): Association and Their Measures in Vedic and Post-Vedic Era
25(1)
2.7 Perception of Cause and Effect as Independent and Dependent Events
26(3)
2.8 Development of Probabilistic Causal Algebra: Evolution of Effect as Measure of Dependence to Probabilistic Cause
29(1)
2.9 Emergence of Measures of Association and Dependence: Correlation and Regression Coefficients
30(1)
2.10 Path Coefficients, Factor Analysis and Principal Components (Karhunen--Loeve Expansion)
31(1)
2.11 Advancements of Concepts and Computations for Associations and Dependence
32(1)
2.12 Discriminant Function and Measures of Dependence
33(2)
2.13 The Default Correlation: Copula
35(1)
2.14 The Apex Vertex of Dynamism (V3)
35(1)
2.15 Markov Chain and Bayesian Inference
36(2)
2.16 The Brownian Motion---Weiner Process
38(2)
2.17 Stochastic Differential Equation: ITO's Process
40(7)
References
41(6)
3 Univariate Normal Distribution and Its Quantile
47(14)
3.1 Probability Distribution
47(2)
3.2 Normal Probability Distribution
49(1)
3.3 Confidence Interval
50(1)
3.4 Quantile and Its Role in Decision-Making
51(3)
3.5 Certainty Equivalent and Quantile
54(7)
References
57(4)
4 Bivariate Normal Distribution and Heuristic-Algorithm of BIVNOR for Generating Biquantile Pairs
61(30)
4.1 Characterization of Joint Cumulative Distribution Function
62(2)
4.2 Bivariate Normal Distribution: Historical Perspectives
64(2)
4.3 Other Properties of Bivariate Normal Distribution
66(3)
4.4 Owen's Computational Scheme for Evaluating Bivariate Normal Integral
69(3)
4.5 Other Methods for Evaluating Bivariate Normal Integral
72(1)
4.6 Software to Generate Tables of Bivariate Normal Quantile (Biquantile) Pairs: Prerequisite for BIVNOR
73(1)
4.7 Multiplicity of Biquantile Pairs: Basics of Heuristics for Developing BIVNOR
74(1)
4.8 Initial Steps of Heuristic BIVNOR
74(1)
4.9 Problems Related to Developing BIVNOR
75(1)
4.10 Algorithm for BIVNOR
75(6)
4.11 Simultaneous (Joint) Confidence Intervals
81(3)
4.11.1 Roy and Bose's Multivariate Confidence Bounds
81(1)
4.11.2 Simultaneous Confidence Interval
81(2)
4.11.3 Bonferroni's Interval
83(1)
4.11.4 Confidence Interval Based on the Chi-Square Quantile
84(1)
4.12 Recent Interests in Biquantile Pairs
84(3)
4.13 Rizopoulos Paradox
87(4)
References
87(4)
5 Software Reliability Testing and Tables Explained
91(12)
5.1 Software Reliability
91(1)
5.2 Evolution of Reliability Testing Criteria
92(2)
5.3 Procedures Adopted to Meet the Evolved Criteria
94(3)
5.4 Generated Tables of Chaps. 8 and 9 Explained
97(6)
5.4.1 Description for Table 8.1 in Chap. 8: Equi-Quantile Values (or BIGH)
97(1)
5.4.2 Description for Table 8.2 of Chap. 8: Iso-Probable Biquantile Pairs of 400 (19 x 21 + 1 = 400) Tables
98(2)
5.4.3 Description of Table 9.1 of Chap. 9 (Tester Table: Owen's Table of T(h, a) Function)
100(1)
5.4.4 Description of Table 9.2 of Chap. 9 (Tester Tables of Biquantile Pairs for Zero Correlation Against Those for Independence Hypothesis)
100(1)
5.4.5 Description of Table 9.3 of Chap. 9 (Tester Tables of Iso-Probable Quantile Pairs for Random Grids of Table 8.1 of Chap. 8)
101(1)
References
102(1)
6 Decision Scenario: Problems and Prospects
103(34)
6.1 Decision Scenario: The Past
104(6)
6.2 Decision Scenario: The Present
110(1)
6.3 Advancements in Decision Processes: Decision Science
111(2)
6.4 Design of Experiment: Designing the Investigation
113(1)
6.5 Decision Function
114(1)
6.6 Discrimination and Classification
115(2)
6.7 Optimization: Linear Programming and Extensions
117(1)
6.8 Basics of Stochastic Programming and Its Chance-Constrained Version
118(5)
6.9 Emergence of Decision Processes Under Risk and Uncertainty
123(3)
6.9.1 Related References
123(1)
6.9.2 Von Neumann and Morgenstern versus Kahneman and Tversky
124(1)
6.9.3 An Attempt for Compromise
125(1)
6.10 Developments in Uncertain Decision-Making
126(4)
6.11 Online Stochastic Combinatorial Optimization
130(2)
6.12 Fuzzy Decision
132(5)
References
133(4)
7 Application Paradigms
137(56)
7.1 Introduction
138(1)
7.2 Comparison Between Simultaneous (Joint) Confidence Intervals
138(9)
7.3 Algorithmic Heuristics for Chance-Constrained Version of Discrimination/Classification
147(4)
7.4 Biquantile in Optimization: Bivariate Joint Chance-Constrained Linear Programming Problem
151(6)
7.5 Bivariate Meteorological Prediction with Equi-quantile Pairs
157(4)
7.6 Equi-quantiles in Bio-statistical Studies
161(1)
7.7 The VaR Measure (The Value at Risk)
162(3)
7.8 Default Correlation: Gaussian Copula Model and Biquantile Pairs
165(2)
7.9 Bivariate Quality Control, Six Sigma Techniques and Biquantile Pairs
167(1)
7.10 Bivariate Stochastic Process and Biquantile Pairs
168(6)
7.11 Simulation and Biquantile Pair/Equi-quantile Value
174(3)
7.12 From Biquantiles to Higgs Boson (God Particle)
177(3)
7.13 Rizopoulos's Paradox (2009)
180(4)
7.13.1 Basics
180(1)
7.13.2 The Paradox: Its Modification and Solution
181(3)
7.13.3 Generalization
184(1)
7.13.4 Reliability and Validity Tests of BIVNOR for Extreme Paradigms
184(1)
7.14 Further Scope for Applications of Biquantiles
184(1)
7.15 Information Gain and Learning
185(8)
7.15.1 Introduction to the Problem
185(2)
7.15.2 Methodology
187(1)
7.15.3 Results
188(1)
References
189(4)
8 Generated Tables by BIVNOR
193(428)
8.1 Table of BIGH the Equi-Quantile Values
193(3)
8.2 Contents for Table 8.2 (Table No. 8.2-1 to 400)
196(425)
9 Tables Generated for Software Testing
621(18)
9.1 The Table of COMP-T to Test Its Equivalence to OWEN's
621(1)
9.2 Tables for Testing BIVNOR COMP. PROB. with JNT. PROB Under Zero Correlation
622(8)
9.3 Tables Generated for Bivariate Normal Iso-Probable Quantile Pairs for TEST CASES
630(6)
9.4 Barycentric Coordinate Reading System: For Analysing Mixed Activities
636(3)
Reference
637(2)
10 Conclusions
639(6)
10.1 Introduction
639(1)
10.2 Conclusions
639(3)
10.3 Caveats and Cautions
642(1)
10.4 The Ultimate Question
642(1)
10.5 Feller's Dictum and Winston's Aspiration
643(2)
References
644(1)
Index 645
N.C. DAS is former professor cum chief scientist at the Department of Statistics and Computer Applications, Birsa Agricultural University, Ranchi. He has over 50 years of teaching and research experience in the field of Statistics, Operations Research and Computer Applications. Earlier, Professor Das worked as the academic secretary cum editor of the Bihar Journal of Mathematics for the period of 1994-98. An active teacher and researcher, Professor Das was a visiting professor of Statistics and Quantitative Methods at the Central University of Jharkhand (Ranchi). He has also been guiding research scholars at the Indian Institute of Coal Management (Ranchi), Indian School of Mines (Dhanbad) and Birla Institute of Technology, Mesra (Ranchi). Presently, Professor Das is the president of the Jharkhand Society of Mathematics as well as of the Jharkhand Society of Statistics (Ranchi).