Statistical techniques for transportation engineering

Statistical techniques for transportation engineering

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...

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Detalles Bibliográficos
Otros Autores: Molugaram, Kumar, author (author), Rao, G. Shanker, author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Oxford, England ; Cambridge, Massachusetts : Butterworth-Heinemann 2017.
Edición:1st edition
Materias:
Transportation engineering.
Transportation engineering > Statistical methods.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630295806719
Tabla de Contenidos:
  • Front Cover
  • Statistical Techniques for Transportation Engineering
  • Copyright Page
  • Contents
  • Preface
  • 1 An Overview of Statistical Applications
  • 1.1 Introduction
  • 1.2 Probability Functions and Statistics
  • 1.2.1 Discrete Versus Continuous Functions
  • 1.2.2 Distributions Describing Randomness
  • 1.2.3 Data Organization
  • 1.2.4 Common Statistical Estimators
  • 1.2.4.1 Measures of Central Tendency
  • 1.2.4.2 Measures of Dispersion
  • 1.3 Applications of Normal Distribution
  • 1.3.1 The Standard Normal Distribution
  • 1.3.2 Characteristics of the Normal Distribution Function
  • 1.4 Confidence Bounds
  • 1.5 Determination of Sample Size
  • 1.6 Random Variables Summation
  • 1.6.1 The Central Limit Theorem
  • 1.6.1.1 Sum of Travel Times
  • 1.6.1.2 Hourly Volumes
  • 1.6.1.3 Sum of Normal Distributions
  • 1.7 The Binomial Distributions
  • 1.7.1 Bernoulli and the Binomial Distribution
  • 1.7.2 Asking People Questions Survey Results
  • 1.7.3 The Binomial and the Normal Distributions
  • 1.8 The Poisson Distribution
  • 1.9 Testing of Hypothesis
  • 1.9.1 Before-and-After Tests With Two Distinct Choices
  • 1.9.1.1 Application: Travel Time Decrease
  • 1.9.1.2 Application: Focus on the Travel Time Difference
  • 1.9.2 Before-and-After Tests With Generalized Alternative Hypothesis
  • 1.9.2.1 An Application: Travel Time Differences
  • 1.9.2.2 One-Sided Versus Two-Sided Tests
  • 1.9.3 Other Useful Statistical Tests
  • 1.9.3.1 The t-Test
  • 1.9.3.2 The F-Test
  • 1.9.3.3 Chi-Square Test: Hypotheses or an Underlying Distribution f(x)
  • 1.10 Summary
  • 2 Preliminaries
  • 2.1 Introduction
  • 2.2 Basic Concepts
  • 2.2.1 Characteristics
  • 2.2.2 Attributes
  • 2.2.3 Variables
  • 2.2.4 Numeric Variables
  • 2.2.5 Categorical Variables
  • 2.2.6 Data
  • 2.2.6.1 Primary Data
  • 2.2.6.2 Secondary Data
  • 2.2.7 Classification and Tabulation.
  • 2.3 Tabulation of Data
  • 2.4 Frequency Distribution
  • 2.4.1 Simple Frequency Distribution
  • 2.4.2 Grouped Frequency Distribution
  • 2.4.2.1 Solved Examples
  • 2.5 Cumulative Frequency Table
  • 2.5.1 Less Than Cumulative Frequency Table
  • 2.5.2 More Than Cumulative Frequency Table
  • 2.6 Measures of Central Tendency
  • 2.7 Arithmetic Mean
  • 2.7.1 Simple Arithmetic Average
  • 2.7.1.1 Shortcut Method (Method of Deviations)
  • 2.7.2 Weighted Arithmetic Mean
  • 2.7.2.1 Combined Arithmetic Mean
  • 2.7.2.1.1 Solved Examples
  • 2.7.3 Merits of Arithmetic Mean
  • 2.7.4 Demerits of Arithmetic Mean
  • 2.7.5 Properties of Mean
  • 2.7.5.1 Solved Examples
  • 2.7.6 Statistical Applications to Transportation Engineering
  • 2.8 Median
  • 2.8.1 Merits of Median
  • 2.8.2 Demerits of Median
  • 2.8.2.1 Solved Examples
  • 2.9 Mode
  • 2.9.1 Merits of Mode
  • 2.9.2 Demerits of Mode
  • 2.9.2.1 Solved Examples
  • 2.10 Geometric Mean
  • 2.10.1 Merits of Geometric Mean
  • 2.10.2 Demerits of Geometric Mean
  • 2.10.2.1 Solved Examples
  • 2.11 Harmonic Mean
  • 2.11.1 Merits of Harmonic Mean
  • 2.11.2 Demerits of Harmonic Mean
  • 2.11.3 Relation Between AM, GM, and HM
  • 2.11.3.1 Solved Examples
  • 2.12 Partition Values (Quartiles, Deciles, and Percentiles)
  • 2.12.1 Quartiles
  • 2.12.2 Deciles
  • 2.12.3 Percentiles
  • 2.13 Measures of Dispersion
  • 2.13.1 Characteristics of an Ideal Measure of Dispersion
  • 2.13.2 Types of Measures of Dispersion
  • 2.14 Range
  • 2.14.1 Coefficient of Range
  • 2.14.2 Merits of Range
  • 2.14.3 Demerits of Range
  • 2.14.4 Uses of Range
  • 2.15 Interquartile Range
  • 2.16 Quartile Deviation
  • 2.16.1 Coefficient of Quartile Deviation
  • 2.16.1.1 Merits of Quartile Deviation
  • 2.16.1.2 Demerits of Quartile Deviation
  • 2.17 Mean Deviation
  • 2.17.1 Coefficient of Mean Deviation
  • 2.17.2 Merits of Mean Deviation.
  • 2.17.3 Demerits of Mean Deviation
  • 2.17.4 Uses of Mean Deviation
  • 2.18 Standard Deviation
  • 2.18.1 Coefficient of Standard Deviation
  • 2.18.2 Merits of Standard Deviation
  • 2.18.3 Demerits of Standard Deviation
  • 2.18.3.1 Uses
  • 3 Probability
  • 3.1 Introduction
  • 3.2 Classical Probability
  • 3.2.1 Properties of Classical Probability
  • 3.2.2 Probability of Failure
  • 3.3 Relative Frequency Approach of Probability
  • 3.4 Symbolic Notation
  • 3.5 Axiomatic Theory of Probability
  • 3.6 Independent and Dependent Events
  • 3.7 Conditional Probability
  • 3.8 Multiplication Theorem on Probability
  • 3.8.1 Solved Examples
  • 3.9 Baye's Theorem
  • 4 Random Variables
  • 4.1 Introduction
  • 4.2 Discrete Random Variable
  • 4.3 Probability Distribution for a Discrete Random Variable
  • 4.3.1 Probability Mass Function
  • 4.3.2 Distribution Function
  • 4.3.3 Additional Properties of Distribution Function
  • 4.4 Mean and Variance of a Discrete Distribution
  • 4.5 Continuous Random Variable
  • 4.6 Probability Density Function
  • 4.7 Cumulative Distribution Function
  • 4.8 Mean and Variance of a Continuous Random Variable
  • 4.8.1 Solved Examples
  • 4.9 Joint Distributions
  • 4.9.1 Joint Probability Function
  • 4.9.2 Joint Probability Distribution of Discrete Random Variables
  • 4.9.3 Marginal Probability Function of a Discrete Random Variables
  • 4.9.4 Joint Distributive Function of Discrete Random Variables
  • 4.10 Conditional Probability Distribution
  • 4.11 Independent Random Variables
  • 4.12 Joint Probability Function of Continuous Random Variables
  • 4.13 Joint Probability Distribution Function of Continuous Random Variables
  • 4.14 Marginal Distribution Function
  • 4.14.1 Marginal Density Functions
  • 4.15 Conditional Probability Density Functions
  • 4.16 Mathematical Expectation and Moments
  • 4.16.1 Properties of Mathematical Expectation.
  • 4.16.2 Variance
  • 4.16.3 Properties of Variance
  • 4.16.4 Covariance
  • 4.17 Moments
  • 4.17.1 Moments About an Arbitrary Number
  • 4.17.2 Moments About Origin
  • 4.17.3 Skewness and Kurtosis
  • 4.18 Moment Generating Function
  • 4.19 Properties of Moment Generating Function
  • 4.19.1 Solved Examples
  • 4.20 Discrete Probability Distributions
  • 4.20.1 Binomial Distribution
  • 4.20.2 Expected Frequencies and Fitting of a Binomial Distribution
  • 4.20.3 Recurrence Relation
  • 4.20.4 Moments, Skewness, and Kurtosis of the Binomial Distribution
  • 4.20.5 Moment Generating Function of a Binomial Distribution
  • 4.20.6 Characteristics of a Binomial Distribution
  • 4.20.6.1 Solved Examples
  • 4.21 Poisson Distribution
  • 4.21.1 Conditions Under Which Poisson Distribution Is Used
  • 4.21.2 Poisson Probability Function
  • 4.21.3 Poisson Frequency Distribution
  • 4.21.4 Moment of a Poisson Distribution
  • 4.21.5 Recurrence Relation
  • 4.21.6 Characteristics of Poisson Distribution
  • 4.21.7 Moment Generating Function of the Poisson Distribution
  • 4.21.8 Reproductive Property of the Poisson Distribution
  • 4.21.8.1 Solved Examples
  • 4.22 Discrete Uniform Distribution
  • 4.23 The Negative Binomial and Geometric Distribution
  • 4.24 Geometric Distribution
  • 4.25 Continuous Probability Distributions
  • 4.25.1 Uniform Distribution
  • 4.25.1.1 Moments of the Uniform Distribution
  • 4.25.1.2 Mean of Uniform Distribution
  • 4.25.1.3 Variance of Uniform Distribution
  • 4.25.1.4 Moment Generating Function of the Uniform Distribution
  • 4.25.2 Exponential and Negative Exponential Distribution
  • 4.26 Normal Distribution
  • 4.26.1 Standard Normal Variable
  • 4.26.2 Distribution Function φ(Z) of Standard Normal Variate
  • 4.26.3 Area Under Normal Curve
  • 4.26.4 Area Under Standard Normal Curve
  • 4.26.5 Properties of Normal Curve
  • 4.26.6 Mean of Normal Distribution.
  • 4.26.7 Variance of Normal Distribution
  • 4.26.8 Mode of Normal Distribution
  • 4.26.9 Median of the Normal Distribution
  • 4.26.10 Moment Generating Function of Normal Distribution With Respect to Origin
  • 4.26.11 Mean Deviation of Normal Distribution
  • 4.26.11.1 Solved Examples
  • 4.26.12 Fitting a Normal Distribution
  • 4.26.13 Linear Combination of Independent Normal Variables
  • 4.26.14 Fitting a Normal Distribution
  • 4.26.15 Normal Approximation to Binomial Distribution
  • 4.27 Characteristic Function
  • 4.28 Gamma Distribution
  • 4.28.1 Mean and Variance of Gamma Distribution
  • 4.28.2 Gamma Distribution of Second Kind
  • 4.29 Beta Distribution of First Kind
  • 4.29.1 Beta Distribution of Second Kind
  • 4.30 Weibull Distribution
  • 5 Curve Fitting
  • 5.1 Introduction
  • 5.2 The Method of Least Squares
  • 5.3 The Least-Squares Line
  • 5.4 Fitting a Parabola by the Method of Least Squares
  • 5.5 Fitting the exponential curve of the form y=a ebx
  • 6 Correlation and Regression
  • 6.1 Introduction
  • 6.2 Correlation
  • 6.2.1 Types of Correlation
  • 6.3 Coefficient of Correlation
  • 6.3.1 Properties of Coefficient of Correlation
  • 6.4 Methods of Finding Coefficient of Correlation
  • 6.5 Scatter Diagram
  • 6.6 Direct Method
  • 6.7 Spearman's Rank Correlation Coefficient
  • 6.7.1 Rank Correlation Coefficient When the Ranks Are Tied
  • 6.8 Calculation of r (Correlation Coefficient) (Karl Pearson's Formula)
  • 6.9 Regression
  • 6.10 Regression Equation
  • 6.11 Curve of Regression
  • 6.12 Types of Regression
  • 6.13 Regression Equations (Linear Fit)
  • 6.13.1 Linear Regression Equation of y on x
  • 6.13.2 Regression Equation of x and y
  • 6.14 Angle between Two Lines of Regression
  • 6.15 Coefficient of Determination
  • 6.16 Coefficient Nondetermination
  • 6.17 Coefficient of Alienation
  • 6.17.1 Solved Examples
  • 6.18 Multilinear Regression.
  • 6.19 Uses of Regression Analysis.

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