Descriptive Statistics for Scientists and Engineers: Applications in R

✍ Scribed by Rajan Chattamvelli, Ramalingam Shanmugam

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 142
• Series: Synthesis Lectures on Mathematics & Statistics
• Edition: 2
• Category: Library

✦ Synopsis

This book introduces descriptive statistics and covers a broad range of topics of interest to students and researchers in various applied science disciplines. This includes measures of location, spread, skewness, and kurtosis; absolute and relative measures; and classification of spread, skewness, and kurtosis measures, L-moment based measures, van Zwet ordering of kurtosis, and multivariate kurtosis. Several novel topics are discussed including the recursive algorithm for sample variance; simplification of complicated summation expressions; updating formulas for sample geometric, harmonic and weighted means; divide-and-conquer algorithms for sample variance and covariance; L-skewness; spectral kurtosis, etc. A large number of exercises are included in each chapter that are drawn from various engineering fields along with examples that are illustrated using the R programming language. Basic concepts are introduced before moving on to computational aspects. Some applicationsin bioinformatics, finance, metallurgy, pharmacokinetics (PK), solid mechanics, and signal processing are briefly discussed. Every analyst who works with numeric data will find the discussion very illuminating and easy to follow.

✦ Table of Contents

Preface
Contents
About the Authors
1 Descriptive Statistics
1.1 Introduction
1.2 Statistics as a Scientific Discipline
1.2.1 Scales of Measurement
1.3 Population Versus Sample
1.3.1 Parameter Versus Statistic
1.4 Combination Notation
1.5 Set-Theoretic Notations
1.6 Summation Notation
1.6.1 Nested Sums
1.6.2 Increment Step Sizes
1.7 Product Notation
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 Testing for Normality
1.11.1 Graphical Methods for Normality Checking
1.11.2 Ogive Plots
1.11.3 P-P and Q-Q Plots
1.11.4 Stem-and-Leaf Plots
1.11.5 Numerical Methods for Normality Testing
1.12 Summary
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
2.11 Exercises
3 Measures of Spread
3.1 Need for a Spread Measure
3.1.1 Categorization of Dispersion Measures
3.2 Sample 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
3.3.2 Degrees of Freedom
3.4 Averaged Absolute Deviation (AAD)
3.4.1 Advantages of Averaged Absolute Deviation
3.4.2 Disadvantages of Averaged Absolute Deviation
3.4.3 Change of Origin and Scale Transformation for AAD
3.5 Variance and Standard Deviation
3.5.1 Volatility
3.5.2 Advantages of Variance
3.5.3 Change of Origin and Scale Transformation for Variance
3.5.4 Disadvantages of Variance
3.5.5 A Bound for Sample Standard Deviation
3.6 Coefficient of Variation
3.6.1 Advantages of Coefficient of Variation
3.6.2 Disadvantages of Coefficient of Variation
3.6.3 An Interpretation of Coefficient of Variation
3.6.4 Change of Origin and Scale for CV
3.7 Gini Coefficient
3.8 Applications
3.9 Summary
3.10 Exercises
4 Skewness
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
4.3.5 Conditional Skewness
4.4 Applications
4.5 Summary
4.6 Exercises
5 Kurtosis
5.1 Concept of Kurtosis
5.1.1 An Interpretation of Kurtosis
5.1.2 Categorization of Kurtosis Measures
5.1.3 Van Zwet ordering of kurtosis
5.2 Measures of Kurtosis
5.2.1 Pearson's Kurtosis Measure
5.2.2 Skewness-Kurtosis Bounds
5.2.3 L-kurtosis
5.2.4 Spectral Kurtosis (SK)
5.2.5 Multivariate Kurtosis
5.2.6 Cokurtosis
5.3 Applications
5.3.1 Detecting Faults using SK
5.4 Summary
5.5 Exercises
A Index
Index