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Statistical Techniques for Transportation Engineering

Book Description

Statistical Techniques for Transportation Engineering is written with a systematic approach in mind and covers a full range of data analysis topics, from the introductory level (basic probability, measures of dispersion, random variable, discrete and continuous distributions) through more generally used techniques (common statistical distributions, hypothesis testing), to advanced analysis and statistical modeling techniques (regression, AnoVa, and time series). The book also provides worked out examples and solved problems for a wide variety of transportation engineering challenges.

  • Demonstrates how to effectively interpret, summarize, and report transportation data using appropriate statistical descriptors
  • Teaches how to identify and apply appropriate analysis methods for transportation data
  • Explains how to evaluate transportation proposals and schemes with statistical rigor

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
  6. Chapter 1. An Overview of Statistical Applications
    1. Abstract
    2. 1.1 Introduction
    3. 1.2 Probability Functions and Statistics
    4. 1.3 Applications of Normal Distribution
    5. 1.4 Confidence Bounds
    6. 1.5 Determination of Sample Size
    7. 1.6 Random Variables Summation
    8. 1.7 The Binomial Distributions
    9. 1.8 The Poisson Distribution
    10. 1.9 Testing of Hypothesis
    11. 1.10 Summary
  7. Chapter 2. Preliminaries
    1. Abstract
    2. 2.1 Introduction
    3. 2.2 Basic Concepts
    4. 2.3 Tabulation of Data
    5. 2.4 Frequency Distribution
    6. 2.5 Cumulative Frequency Table
    7. 2.6 Measures of Central Tendency
    8. 2.7 Arithmetic Mean
    9. 2.8 Median
    10. 2.9 Mode
    11. 2.10 Geometric Mean
    12. 2.11 Harmonic Mean
    13. 2.12 Partition Values (Quartiles, Deciles, and Percentiles)
    14. 2.13 Measures of Dispersion
    15. 2.14 Range
    16. 2.15 Interquartile Range
    17. 2.16 Quartile Deviation
    18. 2.17 Mean Deviation
    19. 2.18 Standard Deviation
  8. Chapter 3. Probability
    1. Abstract
    2. 3.1 Introduction
    3. 3.2 Classical Probability
    4. 3.3 Relative Frequency Approach of Probability
    5. 3.4 Symbolic Notation
    6. 3.5 Axiomatic Theory of Probability
    7. 3.6 Independent and Dependent Events
    8. 3.7 Conditional Probability
    9. 3.8 Multiplication Theorem on Probability
    10. 3.9 Baye’s Theorem
  9. Chapter 4. Random Variables
    1. Abstract
    2. 4.1 Introduction
    3. 4.2 Discrete Random Variable
    4. 4.3 Probability Distribution for a Discrete Random Variable
    5. 4.4 Mean and Variance of a Discrete Distribution
    6. 4.5 Continuous Random Variable
    7. 4.6 Probability Density Function
    8. 4.7 Cumulative Distribution Function
    9. 4.8 Mean and Variance of a Continuous Random Variable
    10. 4.9 Joint Distributions
    11. 4.10 Conditional Probability Distribution
    12. 4.11 Independent Random Variables
    13. 4.12 Joint Probability Function of Continuous Random Variables
    14. 4.13 Joint Probability Distribution Function of Continuous Random Variables
    15. 4.14 Marginal Distribution Function
    16. 4.15 Conditional Probability Density Functions
    17. 4.16 Mathematical Expectation and Moments
    18. 4.17 Moments
    19. 4.18 Moment Generating Function
    20. 4.19 Properties of Moment Generating Function
    21. 4.20 Discrete Probability Distributions
    22. 4.21 Poisson Distribution
    23. 4.22 Discrete Uniform Distribution
    24. 4.23 The Negative Binomial and Geometric Distribution
    25. 4.24 Geometric Distribution
    26. 4.25 Continuous Probability Distributions
    27. 4.26 Normal Distribution
    28. 4.27 Characteristic Function
    29. 4.28 Gamma Distribution
    30. 4.29 Beta Distribution of First Kind
    31. 4.30 Weibull Distribution
  10. Chapter 5. Curve Fitting
    1. Abstract
    2. 5.1 Introduction
    3. 5.2 The Method of Least Squares
    4. 5.3 The Least-Squares Line
    5. 5.4 Fitting a Parabola by the Method of Least Squares
    6. 5.5 Fitting the exponential curve of the form y=a ebx
  11. Chapter 6. Correlation and Regression
    1. Abstract
    2. 6.1 Introduction
    3. 6.2 Correlation
    4. 6.3 Coefficient of Correlation
    5. 6.4 Methods of Finding Coefficient of Correlation
    6. 6.5 Scatter Diagram
    7. 6.6 Direct Method
    8. 6.7 Spearman’s Rank Correlation Coefficient
    9. 6.8 Calculation of r (Correlation Coefficient) (Karl Pearson’s Formula) (Correlation Coefficient) (Karl Pearson’s Formula)
    10. 6.9 Regression
    11. 6.10 Regression Equation
    12. 6.11 Curve of Regression
    13. 6.12 Types of Regression
    14. 6.13 Regression Equations (Linear Fit)
    15. 6.14 Angle between Two Lines of Regression
    16. 6.15 Coefficient of Determination
    17. 6.16 Coefficient Nondetermination
    18. 6.17 Coefficient of Alienation
    19. 6.18 Multilinear Regression
    20. 6.19 Uses of Regression Analysis
  12. Chapter 7. Sampling
    1. Abstract
    2. 7.1 Introduction
    3. 7.2 Population
    4. 7.3 Sample
    5. 7.4 Sampling
    6. 7.5 Random Sampling
    7. 7.6 Simple Random Sampling
    8. 7.7 Stratified Sampling
    9. 7.8 Systematic Sampling
    10. 7.9 Sample Size Determination
    11. 7.10 Sampling Distribution
  13. Chapter 8. Hypothesis Testing
    1. Abstract
    2. 8.1 Introduction
    3. 8.2 Hypothesis
    4. 8.3 Hypothesis Testing
    5. 8.4 Types of Hypothesis
    6. 8.5 Computation of Test Statistic
    7. 8.6 Level of Significance
    8. 8.7 Critical Region
    9. 8.8 One-Tailed Test and Two-Tailed Test
    10. 8.9 Errors
    11. 8.10 Procedure for Hypothesis Testing
    12. 8.11 Important Tests of Hypothesis
    13. 8.12 Critical Values
    14. 8.13 Test of Significance—Large Samples
    15. 8.14 Test of Significance for Single Proportion
    16. 8.15 Testing of Significance for Difference of Proportions
  14. Chapter 9. Chi-Square Distribution
    1. Abstract
    2. 9.1 Introduction
    3. 9.2 Contingency Table
    4. 9.3 Calculation of Expected Frequencies
    5. 9.4 Chi-Square Distribution
    6. 9.5 Mean and Variance of Chi-Square
    7. 9.6 Additive Property of Independent Chi-Square Variate
    8. 9.7 Degrees of Freedom
    9. 9.8 Conditions for Using Chi-Square Test
    10. 9.9 Uses of Chi-Square Test
  15. Chapter 10. Test of Significance—Small Samples
    1. Abstract
    2. 10.1 Introduction
    3. 10.2 Moments About Mean
    4. 10.3 Properties of Probability Curve
    5. 10.4 Assumptions for t-Test
    6. 10.5 Uses of t-Distribution
    7. 10.6 Interval Estimate of Population Mean
    8. 10.7 Types of t-Test
    9. 10.8 Significant Values of t
    10. 10.9 Test of Significance of a Single Mean
    11. 10.10 Student’s t-Test for Difference of Means
    12. 10.11 Paired t-Test
    13. 10.12 F-Distribution
  16. Chapter 11. ANOVA (Analysis of Variance)
    1. Abstract
    2. 11.1 Introduction
    3. 11.2 Assumptions
    4. 11.3 One-Way ANOVA
    5. 11.4 Working Rule
  17. Chapter 12. Analysis of Time Series
    1. Abstract
    2. 12.1 Introduction
    3. 12.2 Purpose of Time Series Study
    4. 12.3 Editing of Data
    5. 12.4 Components of Time Series
    6. 12.5 Mathematical Model for a Time Series
    7. 12.6 Methods of Measuring Trend
  18. Chapter 13. Index Numbers
    1. Abstract
    2. 13.1 Introduction
    3. 13.2 Definitions and Characteristics
    4. 13.3 Types of Index Numbers
    5. 13.4 Problems in the Construction of Index Numbers
    6. 13.5 Method of Constructing Index Numbers
    7. 13.6 Tests for Consistency of Index Numbers
    8. 13.7 Quantity Index Numbers
    9. 13.8 Consumer Price Index Number
    10. 13.9 Chain Base Method
    11. 13.10 Base Conversion
    12. 13.11 Splicing
    13. 13.12 Deflation
  19. Index