Statistics. Volume 3, Categorical and time dependent data analysis

Contents
Preface
Chapter 1
Customer Satisfaction Analysis
	Abstract
	1. Introduction
	2. Questionnaire
	3. Fundamental Parameters
	4. Correlation Factor Testing
	5. Normalization of the Variables
	6. Improve Requested and Contributed Items
	7. CS Correlation Factor
	8. Target Value for Satisfactions of Explanatory  and Objective Variables
	9. Analysis for Sub Group
	10. CS Analysis Using Multiple Regression
	11. Interaction between Explanatory Variables
	12. Extended Normalized Correlation Factor
	13. Treatment of Correlation Factor
	14. Summary
Chapter 2
Independent Factor Analysis
	Abstract
	1. Introduction
	2. Questionnaire
	3. Independent Value
	4. Testing
	5. Independent Factor
	6. Adjust Residuals
	7. Level Achievement Ratio
	8. Determination of Item Based on CS Analysis
		8.1. Normalization
		8.2. Improve Requested and Contributed Items
	9. CS Correlation Factor
	10. Expected Objective Variable Improvement  with Improving Explanatory Value
		10.1. Two Levels (Objective Variable)-Two Levels (Explanatory)
		10.2. General Form for Expected Objective Variable Level
	11. Analysis for Sub Group
	Summary
Chapter 3
Statistical Testing and Predictions
	Abstract
	1. Introduction
	2. Hypothesis
	3. Level of Significance
	4. P Points for Various Probability Distributions
	5. Testing for One Variable
		5.1. One Sample Data Testing for Known Variance
			Hypothesis
			Evaluation and Judgment
			Prediction
		5.2. Sample Average Testing for Known Variance
			Hypothesis
			Evaluation and Judgment
			Prediction
		5.3. Sample Average Testing for Unknown Variance
			Hypothesis
			Evaluation and Judgment
			Prediction
				(Example)
		5.4. Sample Variance Testing for Known Variance
			Hypothesis
			Evaluation and Judgment
			Prediction
		5.5. Outliers Testing
		5.6. Population Ratio Testing with Restored Extraction
			Hypothesis
			Evaluation and Judgment
			Prediction
		5.7. Population Ratio Testing with Non-Restored Extraction
			Hypothesis
			Evaluation and Judgment
			Prediction
	6. Testing for Two Variables
		6.1. Testing of Difference Between Population Averages:  Is Known
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.2. Testing of Difference between Population Averages:  Is Unknown  and the Variances Are Assumed to Be the Same
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.3. Testing of Difference between Population Averages:  Is  Unknown and the Variances Are Assumed to Be Different
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.4. Testing of Difference between Population Averages:  Is  Unknown with Paired Data
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.5. Testing of Difference between Population Ratio with Restored Extraction
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.6. Testing of Difference between Population Ratio  with Non-Restored Extraction
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.7. Testing of Ratio of Two Population’s Variances: and  Are Known
			Hypothesis
			Evaluation and Judgment
			Prediction
		6.8. Testing of Ratio of Two Population’s Variances  and   Are Unknown
			Hypothesis
			Evaluation and Judgment
			Prediction
	7. Testing for Correlation Factors
		7.1. Correlation Factor Testing
			Hypothesis
			Evaluation and Judgment
			Prediction
		7.2. Correlation Factor Testing for Reference One
			Hypothesis
			Evaluation and Judgment
			Prediction
		7.3. Two Correlation Factor Testing
			Hypothesis
			Evaluation and Judgment
			Prediction
	8. Testing for Regression
		Hypothesis
		Evaluation and Judgment
		Prediction
	9. Testing for Multi Regression
		Hypothesis
		Evaluation and Judgment
		Prediction
	10. Testing for Effectiveness of Variances in  Multi Regression
		Hypothesis
		Evaluation and Judgment
		Prediction
	11. Testing for Variance Analysis
		11.1. One Way Analysis
			Hypothesis
			Evaluation and Judgment
			Prediction
		11.2. Two Way Analysis without Repeated Data
			Hypothesis
			Evaluation and Judgment
			Prediction
		11.3. Two Way Analysis with Repeated Data
			Hypothesis
			Evaluation and Judgment
			Prediction
		11.4. Independent Factor Analysis
			Hypothesis
			Evaluation and Judgment
			Prediction
Chapter 4
Score Evaluation
	Abstract
	1. Introduction
	2. Evaluation of the Five Subjects
	3. Score Evaluation Considering Standard Deviation
	Summary
Chapter 5
AHP (Analytic Hierarchy Process)
	Abstract
	1. Introduction
	2. AHP Process
	3. Pair Comparison Method
		3.1. Pair Comparison Table
		3.2. Weight Evaluation Based on Geometric Average
		3.3. Eigenvector Method
	4. Consistency Check of Pair Comparison
	Summary
Chapter 6
Quantification Theory I
	Abstract
	1. Introduction
	2. One Variable Analysis
	3. Analysis with Many Variables
	4. Mixture of Numerical and Categorical Data  for Explanation Variables
	Summary
Chapter 7
Quantification Theory II
	Abstract
	1. Introduction
	2. Discriminant Analysis with One Categorical Data
		Healthy Member Data
		Disease Member Data
	3. Discriminant Analysis with Two Categorical Data
	Summary
Chapter 8
Quantification Theory III  (Correspondence Analysis)
	Abstract
	1. Introduction
	2. Basic Concept of Quantification Theory III
	3. General Form Data for Correspondence Analysis
	Summary
Chapter 9
Quantification Theory IV
	Abstract
	1. Introduction
	2. Analytical Process
	Summary
Chapter 10
Survival Time Probability
	Abstract
	1. Introduction
	2. Survival Probability
	3. Different Expression of Survival Probability
	4. Survival Probability with Incomplete Data  (Kaplan-Meier Predictive Method)
	5. Regression for Survival Probability
		5.1. Exponential Function Regression
		5.2. Weibull Function Regression
	6. Average and Standard Deviation of Survival Time
	7. Hazard Model
		7.1. Definition of Hazard Function
		7.2. Analytical Expression for Hazard Function  (Exponential Approximation)
		7.3. Analytical Expression for Hazard Function (Weibull Function)
	8. Testing of Two Group Survival Time
	Summary
Chapter 11
Population Prediction
	Abstract
	1. Introduction
	2. Population in Future
	Summary
Chapter 12
Random Walk
	Abstract
	1. Introduction
	2. Fundamental Analysis for Random Walk
		2.1. General Theory for Evaluating a Case Number of Path
		2.2. Principle of Symmetry
		2.3. The Path Number Where All Points Except for the Starting Point  Is Positive
		2.4. The Number of Path from to  Where
		2.5. The Path Number from to Where
	3. The Probability That a Person Is in Positive Region
		3.1. The Probability Where the Path Starts from  to
		3.2. The Probability That a Person Reaches  Axis at 2n Trial for the  First Time
		3.3. The Probability That a Person Enters a Negative Region at  Time Step for the First Time
		3.4. The Probability That a Person Does Not Cross X Axis up to   Time Step
		3.5. The Probability That a Person Does Not Enter Negative Region up to  Time Steps
		3.6. The Probability That the Length of  Is in Positive Region of 2n  Length Path
	4. Return Frequency to the Origin
	Summary
Chapter 13
A Markov Process
	Abstract
	1. Introduction
	2. A Markov Process for Random Walk
	3. Transition Probability for Random Walk
	4. Transition Matrix Elements
		4.1. General Discussion for Matrix Elements
		4.2. Supply Source
		4.3. Supply Source Included in the Transition Matrix
		4.4. Vanishing Monitor
		4.5. Constant Flux
		4.6. Initial Condition
	5. Various Examples
		5.1. Promotion of University Student Grade
		5.2. Promotion of University Grade in the Steady State
		5.3. Population Problem
		5.4. Share Rate of a Product
		5.5. Repeat Customer
		5.6. Queue with Single Teller Window
			Let us consider a status of 0.
			We consider the status 1.
			We consider status 6.
		5.7. Queue with Multi Teller Windows
			Let us consider the status of 0.
			We consider the status 1.
			We consider the status 2.
			We consider the status 3.
			We consider the status 6.
		5.8. Blood Type Transition
	6. Status after Long Time Steps
		6.1. Status after N Step
		6.2. Steady State
		6.3. Vanishing Process
	7. A Network Loop
		7.1. Network Matrix
		7.2. A Network Path with a Loop
	Summary
Chapter 14
Random Number
	Abstract
	1. Introduction
	2. Characteristics of Random Number
		Characteristic 1: Principle of Equal A Priori Probabilities
		Characteristic 2: No Regularity
	3. Uniform Random Number Series
	4. Numerical Uniform Random Number Generation Method
	5. Testing of Random Number Series
		5.1. Testing of Equal Priori Probabilities
		5.2. Testing of No Regularity
		Combination Testing
			Runs Testing
	6. Random Number Series Associated with Various Probability Distributions
	7. Inverse Type Random Number Generation for General Probability Function
	8. Random Number Series for Exponential Distribution
	9. Random Number Series for Poisson Distribution
	10. Random Number Series for a Normal Distribution
	11. Random Number Series for Natural Numbers  between 1 and N
	12. Two Random Numbers That Follow Normal Distributions with a Correlation Factor of
	Summary
Chapter 15
Matrix Operation
	Abstract
	1. Introduction
	2. Definition of a Matrix
	3. Sum of a Matrix
	4. Product of a Constant Number and a Matrix
	5. A Product of Two Matrices Related to a  Simultaneous Equations
	6. Transverse Matrix
	7. Solution of a Simultaneous Equations
	8. Gauss Elimination Method
		8.1. Gauss Elimination Method and LU Decomposition
		8.2. LU Division
		8.3. Inverse Matrix Derivation Utilizing LU Division
	9. Determinant of a Matrix
	10. Numerical Evaluation of Eigenvalue
		10.1. Relationship between Matrix and Eigenvector
		10.2. Power Method
	11. Jacobi Method for Symmetrical Matrix
	12. n-th Product of Matrix
Appendix 1
Related Mathematics
	1. Summation  and Product
	2. A Gamma Function and a Beta Function
		2.1. Definition of a Gamma Function
		2.2. A Gamma Function and a Factorial
		2.3. Evaluation of
		2.4. A Gamma Function Where x < 0
		2.5. A Product of a Gamma Function of
		2.6. A Binominal Factor for
		2.7. A Beta Function
	3. Gauss Integration
		3.1. Normal Gauss Integration
		3.2. Modified Gauss Integration
	4. An Error Function
	5. An Integral Area of Converted Variables
	6. A Marginal Probability Distribution
	7. Integration by Parts
	8. Derivatives of Inverse Trigonometric Functions
	9. A Derivative Function
	10. Vector Derivative
	11. Symmetry of the Matrix
	12. A Stirling’s Formula
		Step 1: A Wallis’ formula
		Step 2:
		Step 3:
	13. Trigonometric Functions
Appendix 2
Summary of Probability Distributions  and Their Moments
	Abstract
	1. Introduction
	2. General Relationships
	3. Functions, Generating Functions, and Moments Parameters for Various Probability Distributions
		3.1. A Uniform Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.2. A Binomial Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.3. A Multinomial Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.4. A Negative Binomial Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.5. A Beta Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.6. A Dirichlet Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.7. A Gamma Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.8. An Inverse Gamma Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.9. A Poisson Distribution
			Graphics
			Probability Function
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.10. A Geometric Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.11. A Hypergeometric Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.12. A Normal Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.13. A Standard Normal Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.14. A Lognormal Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.15. A Cauchy Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.16.  Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.17.  Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.18. A Rayleigh Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.19. An F Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.20. A t Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.21. An Exponential Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.22. An Erlang Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.23. A Laplace Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
		3.24. A Weibull Distribution
			Graphics
			Probability Distribution
			Generating Function
			Moments
			Central Moments
			Moment Parameters
			Peak Position
			Comment
References
About the Author
Index
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