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by Naresh Davergave, Anil Shah, G Rao, Kumar Molugaram
Statistical Techniques for Transportation Engineering
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Title page
Table of Contents
Copyright
Preface
Chapter 1. An Overview of Statistical Applications
Abstract
1.1 Introduction
1.2 Probability Functions and Statistics
1.3 Applications of Normal Distribution
1.4 Confidence Bounds
1.5 Determination of Sample Size
1.6 Random Variables Summation
1.7 The Binomial Distributions
1.8 The Poisson Distribution
1.9 Testing of Hypothesis
1.10 Summary
Chapter 2. Preliminaries
Abstract
2.1 Introduction
2.2 Basic Concepts
2.3 Tabulation of Data
2.4 Frequency Distribution
2.5 Cumulative Frequency Table
2.6 Measures of Central Tendency
2.7 Arithmetic Mean
2.8 Median
2.9 Mode
2.10 Geometric Mean
2.11 Harmonic Mean
2.12 Partition Values (Quartiles, Deciles, and Percentiles)
2.13 Measures of Dispersion
2.14 Range
2.15 Interquartile Range
2.16 Quartile Deviation
2.17 Mean Deviation
2.18 Standard Deviation
Chapter 3. Probability
Abstract
3.1 Introduction
3.2 Classical Probability
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
3.9 Baye’s Theorem
Chapter 4. Random Variables
Abstract
4.1 Introduction
4.2 Discrete Random Variable
4.3 Probability Distribution for a Discrete Random Variable
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
4.9 Joint Distributions
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
4.15 Conditional Probability Density Functions
4.16 Mathematical Expectation and Moments
4.17 Moments
4.18 Moment Generating Function
4.19 Properties of Moment Generating Function
4.20 Discrete Probability Distributions
4.21 Poisson Distribution
4.22 Discrete Uniform Distribution
4.23 The Negative Binomial and Geometric Distribution
4.24 Geometric Distribution
4.25 Continuous Probability Distributions
4.26 Normal Distribution
4.27 Characteristic Function
4.28 Gamma Distribution
4.29 Beta Distribution of First Kind
4.30 Weibull Distribution
Chapter 5. Curve Fitting
Abstract
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
Chapter 6. Correlation and Regression
Abstract
6.1 Introduction
6.2 Correlation
6.3 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
6.8 Calculation of r (Correlation Coefficient) (Karl Pearson’s Formula) (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)
6.14 Angle between Two Lines of Regression
6.15 Coefficient of Determination
6.16 Coefficient Nondetermination
6.17 Coefficient of Alienation
6.18 Multilinear Regression
6.19 Uses of Regression Analysis
Chapter 7. Sampling
Abstract
7.1 Introduction
7.2 Population
7.3 Sample
7.4 Sampling
7.5 Random Sampling
7.6 Simple Random Sampling
7.7 Stratified Sampling
7.8 Systematic Sampling
7.9 Sample Size Determination
7.10 Sampling Distribution
Chapter 8. Hypothesis Testing
Abstract
8.1 Introduction
8.2 Hypothesis
8.3 Hypothesis Testing
8.4 Types of Hypothesis
8.5 Computation of Test Statistic
8.6 Level of Significance
8.7 Critical Region
8.8 One-Tailed Test and Two-Tailed Test
8.9 Errors
8.10 Procedure for Hypothesis Testing
8.11 Important Tests of Hypothesis
8.12 Critical Values
8.13 Test of Significance—Large Samples
8.14 Test of Significance for Single Proportion
8.15 Testing of Significance for Difference of Proportions
Chapter 9. Chi-Square Distribution
Abstract
9.1 Introduction
9.2 Contingency Table
9.3 Calculation of Expected Frequencies
9.4 Chi-Square Distribution
9.5 Mean and Variance of Chi-Square
9.6 Additive Property of Independent Chi-Square Variate
9.7 Degrees of Freedom
9.8 Conditions for Using Chi-Square Test
9.9 Uses of Chi-Square Test
Chapter 10. Test of Significance—Small Samples
Abstract
10.1 Introduction
10.2 Moments About Mean
10.3 Properties of Probability Curve
10.4 Assumptions for t-Test
10.5 Uses of t-Distribution
10.6 Interval Estimate of Population Mean
10.7 Types of t-Test
10.8 Significant Values of t
10.9 Test of Significance of a Single Mean
10.10 Student’s t-Test for Difference of Means
10.11 Paired t-Test
10.12 F-Distribution
Chapter 11. ANOVA (Analysis of Variance)
Abstract
11.1 Introduction
11.2 Assumptions
11.3 One-Way ANOVA
11.4 Working Rule
Chapter 12. Analysis of Time Series
Abstract
12.1 Introduction
12.2 Purpose of Time Series Study
12.3 Editing of Data
12.4 Components of Time Series
12.5 Mathematical Model for a Time Series
12.6 Methods of Measuring Trend
Chapter 13. Index Numbers
Abstract
13.1 Introduction
13.2 Definitions and Characteristics
13.3 Types of Index Numbers
13.4 Problems in the Construction of Index Numbers
13.5 Method of Constructing Index Numbers
13.6 Tests for Consistency of Index Numbers
13.7 Quantity Index Numbers
13.8 Consumer Price Index Number
13.9 Chain Base Method
13.10 Base Conversion
13.11 Splicing
13.12 Deflation
Index
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