Cover -- Title Page -- Copyright -- Contents -- Preface -- About The Companion Website -- Chapter 1 Descriptive Statistics -- 1.1 Introduction -- 1.2 Statistics as A Scientific Discipline -- 1.2.1 Scales of Measurement -- 1.3 The NOIR Scale -- 1.3.1 The Nominal Scale -- 1.3.2 The Ordinal Scale -- 1.3.3 The Interval Scale -- 1.3.4 The Ratio Scale -- 1.4 Population Versus Sample -- 1.4.1 Parameter Versus Statistic -- 1.5 Combination Notation -- 1.6 Summation Notation -- 1.6.1 Nested Sums -- 1.6.2 Increment Step Sizes -- 1.7 Product Notation -- 1.7.1 Evaluating Large Powers -- 1.8 Rising and Falling Factorials -- 1.9 Moments and Cumulants -- 1.10 Data Transformations -- 1.10.1 Change of Origin -- 1.10.2 Change of Scale -- 1.10.3 Change of Origin and Scale -- 1.10.4 Min-Max Transformation -- 1.10.5 Nonlinear Transformations -- 1.10.6 Standard Normalization -- 1.11 Data Discretization -- 1.12 Categorization of Data Discretization -- 1.12.1 Equal Interval Binning (EIB) -- 1.12.2 Equal Frequency Binning (EFB) -- 1.12.3 Entropy-Based Discretization (EBD) -- 1.12.4 Error in Discretization -- 1.13 Testing for Normality -- 1.13.1 Graphical Methods for Normality Checking -- 1.13.2 Ogive Plots -- 1.13.3 P-P and Q-Q Plots -- 1.13.4 Stem-and-Leaf Plots -- 1.13.5 Numerical Methods for Normality Testing -- 1.14 Summary -- Chapter 2 Measures of Location -- 2.1 Meaning of Location Measure -- 2.1.1 Categorization of Location Measures -- 2.2 Measures of Central Tendency -- 2.3 Arithmetic Mean -- 2.3.1 Updating Formula For Sample Mean -- 2.3.2 Sample Mean Using Change of Origin and Scale -- 2.3.3 Trimmed Mean -- 2.3.4 Weighted Mean -- 2.3.5 Mean of Grouped Data -- 2.3.6 Updating Formula for Weighted Sample Mean -- 2.3.7 Advantages of Mean -- 2.3.8 Properties of The Mean -- 2.4 Median -- 2.4.1 Median of Grouped Data.

2.5 Quartiles and Percentiles -- 2.6 MODE -- 2.6.1 Advantages of Mode -- 2.7 Geometric Mean -- 2.7.1 Updating Formula For Geometric Mean -- 2.8 Harmonic Mean -- 2.8.1 Updating Formula For Harmonic Mean -- 2.9 Which Measure to Use? -- 2.10 Summary -- Chapter 3 Measures of Spread -- 3.1 Need For a Spread Measure -- 3.1.1 Categorization of Dispersion Measures -- 3.2 RANGE -- 3.2.1 Advantages of Range -- 3.2.2 Disadvantage of Range -- 3.2.3 Applications of Range -- 3.3 Inter-Quartile Range (IQR) -- 3.3.1 Change of Origin and Scale Transformation for Range -- 3.4 The Concept of Degrees of Freedom -- 3.5 Averaged Absolute Deviation (AAD) -- 3.5.1 Advantages of Averaged Absolute Deviation -- 3.5.2 Disadvantages of Averaged Absolute Deviation -- 3.5.3 Change of Origin and Scale Transformation for AAD -- 3.6 Variance and Standard Deviation -- 3.6.1 Advantages of Variance -- 3.6.2 Change of Origin and Scale Transformation for Variance -- 3.6.3 Disadvantages of Variance -- 3.6.4 A Bound for Sample Standard Deviation -- 3.7 Coefficient of Variation -- 3.7.1 Advantages of Coefficient of Variation -- 3.7.2 Disadvantages of Coefficient of Variation -- 3.7.3 An Interpretation of Coefficient of Variation -- 3.7.4 Change of Origin and Scale for CV -- 3.8 Gini Coefficient -- 3.9 Summary -- Chapter 4 Skewness and Kurtosis -- 4.1 Meaning of Skewness -- 4.1.1 Absolute Versus Relative Measures of Skewness -- 4.2 Categorization of Skewness Measures -- 4.3 Measures of Skewness -- 4.3.1 Bowley's Skewness Measure -- 4.3.2 Pearson's Skewness Measure -- 4.3.3 Coefficient of Quartile Deviation -- 4.3.4 Other Skewness Measures -- 4.4 Concept of Kurtosis -- 4.4.1 An Interpretation of Kurtosis -- 4.4.2 Categorization of Kurtosis Measures -- 4.5 Measures of Kurtosis -- 4.5.1 Pearson's Kurtosis Measure -- 4.5.2 Skewness-Kurtosis Bounds -- 4.5.3 L-kurtosis.

4.5.4 Spectral Kurtosis (SK) -- 4.5.5 Detecting Faults Using SK -- 4.5.6 Multivariate Kurtosis -- 4.6 Summary -- Chapter 5 Probability -- 5.1 Introduction -- 5.2 Probability -- 5.3 Different Ways to Express Probability -- 5.3.1 Converting Nonrepeating Decimals to Fractions -- 5.3.2 Converting Repeating Decimals to Fractions -- 5.3.3 Converting Tail-Repeating Decimals to Fractions -- 5.4 Sample Space -- 5.5 Mathematical Background -- 5.5.1 Sets and Mappings -- 5.5.2 Venn Diagrams -- 5.5.3 Tree Diagrams -- 5.5.4 Bipartite Graphs -- 5.5.5 Bipartite Forests -- 5.6 Events -- 5.6.1 Deterministic and Probabilistic Events -- 5.6.2 Discrete Versus Continuous Events -- 5.6.3 Event Categories -- 5.6.4 Do-Little Principle for Events -- 5.7 Event Algebra -- 5.7.1 Laws of Events -- 5.7.2 De'Morgan's Laws -- 5.8 Basic Counting Principles -- 5.8.1 Rule of Sums (ROS) -- 5.8.2 Principle of Counting (POC) -- 5.8.3 Complete Enumeration -- 5.9 Permutations and Combinations -- 5.9.1 Permutations with Restrictions -- 5.9.2 Permutation of Alike Objects -- 5.9.3 Cyclic Permutations -- 5.9.4 Cyclic Permutations of Subsets -- 5.9.5 Combinations -- 5.10 Principle of Inclusion and Exclusion (PIE) -- 5.11 Recurrence Relations -- 5.11.1 Derangements and Matching Problems -- 5.12 Urn Models -- 5.13 Partitions -- 5.14 Axiomatic Approach -- 5.14.1 Probability Measure -- 5.14.2 Probability Space -- 5.15 The Classical Approach -- 5.15.1 Counting Techniques in Classical Probability -- 5.15.2 Assigning Probabilities to Events -- 5.15.3 Rules of Probability -- 5.15.4 Do-Little Principle of Probability -- 5.15.5 Permutation and Combination in Classical Approach -- 5.15.6 Sequentially Dependent Events -- 5.15.7 Independence of Events -- 5.15.8 Independent Random Variables -- 5.16 Frequency Approach -- 5.16.1 Entropy Versus Probability -- 5.17 Bayes Theorem.

5.17.1 Bayes Theorem for Conditional Probability -- 5.17.2 Bayes Classification Rule -- 5.18 Summary -- Chapter 6 Discrete Distributions -- 6.1 Discrete Random Variables -- 6.2 Binomial Theorem -- 6.2.1 Recurrence Relation for Binomial Coefficients -- 6.2.2 Distributions Obtainable from Binomial Theorem -- 6.3 Mean Deviation of Discrete Distributions -- 6.3.1 Recurrence Relation for Mean Deviation -- 6.4 Bernoulli Distribution -- 6.5 Binomial Distribution -- 6.5.1 Properties of Binomial Distribution -- 6.5.2 Moment Recurrences -- 6.5.3 Additivity Property -- 6.5.4 Distribution of the Difference of Successes and Failures -- 6.5.5 Algorithm for Binomial Distribution -- 6.5.6 Tail Probabilities -- 6.5.7 Approximations -- 6.5.8 Limiting Form of Binomial Distribution -- 6.6 Discrete Uniform Distribution -- 6.6.1 Properties of Discrete Uniform Distribution -- 6.6.2 An Application -- 6.7 Geometric Distribution -- 6.7.1 Properties of Geometric Distribution -- 6.7.2 Memory-less Property -- 6.7.3 Tail Probabilities -- 6.7.4 Random Samples -- 6.8 Negative Binomial Distribution -- 6.8.1 Properties of Negative Binomial Distribution -- 6.8.2 Moment Recurrence -- 6.8.3 Tail Probabilities -- 6.9 Poisson Distribution -- 6.9.1 Properties of Poisson Distribution -- 6.9.2 Algorithms for Poisson Distribution -- 6.9.3 Truncated Poisson Distribution -- 6.10 Hypergeometric Distribution -- 6.10.1 Properties of Hypergeometric Distribution -- 6.10.2 Moments of Hypergeometric Distribution -- 6.10.3 Approximations for Hypergeometric Distribution -- 6.11 Negative Hypergeometric Distribution -- 6.12 Beta Binomial Distribution -- 6.13 Logarithmic Series Distribution -- 6.13.1 Properties of Logarithmic Distribution -- 6.14 Multinomial Distribution -- 6.14.1 Properties of Multinomial Distribution -- 6.15 Summary.

Chapter 7 Continuous Distributions -- 7.1 Introduction -- 7.2 Mean Deviation of Continuous Distributions -- 7.2.1 Notion of Infinity -- 7.3 Continuous Uniform Distribution -- 7.3.1 Properties of Continuous Uniform Distribution -- 7.3.2 Relationships with Other Distributions -- 7.3.3 Applications -- 7.4 Exponential Distribution -- 7.4.1 Properties of Exponential Distribution -- 7.4.2 Additivity Property -- 7.5 Beta Distribution -- 7.5.1 Type-I Beta Distribution -- 7.5.2 Properties of Type-I Beta Distribution -- 7.5.3 Type-II Beta Distribution -- 7.5.4 Properties of Type-II Beta Distribution -- 7.5.5 Relationship with Other Distributions -- 7.6 The Incomplete Beta Function -- 7.6.1 Tail Areas Using IBF -- 7.6.2 Tables -- 7.7 General Beta Distribution -- 7.8 Arc-Sine Distribution -- 7.8.1 Properties of Arc-Sine Distribution -- 7.9 Gamma Distribution -- 7.9.1 Properties of Gamma Distribution -- 7.9.2 Relationships with Other Distributions -- 7.9.3 Incomplete Gamma Function (IGF) -- 7.10 Cosine Distribution -- 7.11 The Normal Distribution -- 7.11.1 Properties of Normal Distribution -- 7.11.2 Transformations to Normality -- 7.11.3 Functions of Normal Variates -- 7.11.4 Relation to Other Distributions -- 7.11.5 Algorithms -- 7.12 Cauchy Distribution -- 7.12.1 Properties of Cauchy Distribution -- 7.12.2 Functions of Cauchy Variate -- 7.12.3 Relation to Other Distributions -- 7.13 Inverse Gaussian Distribution -- 7.13.1 Relation to Other Distributions -- 7.14 Lognormal Distribution -- 7.14.1 Properties of Lognormal Distribution -- 7.14.2 Moments -- 7.14.3 Fitting Lognormal Distribution -- 7.15 Pareto Distribution -- 7.15.1 Properties of Pareto Distribution -- 7.15.2 Relation to Other Distributions -- 7.15.3 Algorithms -- 7.16 Double Exponential Distribution -- 7.16.1 Relation to Other Distributions.

7.17 Central X2 Distribution.