Statistics for Scientists and Engineers

Ramalingam Shanmugam is the Editor-in-Chief for the journals: Advances in Life Sciences and Health, International Journal of Research in Medical Sciences, and Global Journal of Research and Review. He is the Book-Review Editor of the Journal of Statistical Computation and Simulation. He directed Statistics Consulting Center in the Mississippi State University. He served the Argonne National Lab., University of Colorado, University of South Alabama and the Indian Statistical Institute. He has published 120 research articles and is a fellow of the International Statistical Institute. Currently, he is a professor in the School of Health Administration, Texas State University. He is a recipient of several research awards from the Texas State University.Rajan Chattamvelli has worked as an Analyst Specialist at Denver Public Health and was a visiting professor at the Indian Institute of Management. He was Chair of the Department of Computer Applications at Presidency College and Periyar Maniammai University, India.

• Preface xvAbout The Companion Website xxi1 Descriptive Statistics 11.1 Introduction 11.2 Statistics as A Scientific Discipline 31.3 The NOIR Scale 61.4 Population Versus Sample 81.5 Combination Notation 111.6 Summation Notation 111.7 Product Notation 191.8 Rising and Falling Factorials 221.9 Moments and Cumulants 221.10 Data Transformations 231.11 Data Discretization 281.12 Categorization of Data Discretization 281.13 Testing for Normality 341.14 Summary 382 Measures of Location 432.1 Meaning of Location Measure 432.2 Measures of Central Tendency 442.3 Arithmetic Mean 452.4 Median 542.5 Quartiles and Percentiles 572.6 MODE 582.7 Geometric Mean 592.8 Harmonic Mean 612.9 Which Measure to Use? 632.10 Summary 633 Measures of Spread 673.1 Need For a Spread Measure 673.2 RANGE 713.3 Inter-Quartile Range (IQR) 733.4 The Concept of Degrees of Freedom 743.5 Averaged Absolute Deviation (AAD) 763.6 Variance and Standard Deviation 773.7 Coefficient of Variation 823.8 Gini Coefficient 843.9 Summary 844 Skewness and Kurtosis 894.1 Meaning of Skewness 894.2 Categorization of Skewness Measures 934.3 Measures of Skewness 944.4 Concept of Kurtosis 994.5 Measures of Kurtosis 1024.6 Summary 1075 Probability 1115.1 Introduction 1115.2 Probability 1125.3 Different Ways to Express Probability 1145.4 Sample Space 1195.5 Mathematical Background 1215.6 Events 1275.7 Event Algebra 1325.8 Basic Counting Principles 1355.9 Permutations and Combinations 1405.10 Principle of Inclusion and Exclusion (PIE) 1475.11 Recurrence Relations 1495.12 Urn Models 1525.13 Partitions 1545.14 Axiomatic Approach 1545.15 The Classical Approach 1565.16 Frequency Approach 1665.17 Bayes Theorem 1685.18 Summary 1736 Discrete Distributions 1856.1 Discrete Random Variables 1856.2 Binomial Theorem 1866.3 Mean Deviation of Discrete Distributions 1896.4 Bernoulli Distribution 1926.5 Binomial Distribution 1946.6 Discrete Uniform Distribution 2116.7 Geometric Distribution 2146.8 Negative Binomial Distribution 2236.9 Poisson Distribution 2296.10 Hypergeometric Distribution 2386.11 Negative Hypergeometric Distribution 2416.12 Beta Binomial Distribution 2416.13 Logarithmic Series Distribution 2426.14 Multinomial Distribution 2436.15 Summary 2467 Continuous Distributions 2557.1 Introduction 2557.2 Mean Deviation of Continuous Distributions 2567.3 Continuous Uniform Distribution 2607.4 Exponential Distribution 2657.5 Beta Distribution 2697.6 The Incomplete Beta Function 2767.7 General Beta Distribution 2787.8 Arc-Sine Distribution 2797.9 Gamma Distribution 2827.10 Cosine Distribution 2857.11 The Normal Distribution 2867.12 Cauchy Distribution 2937.13 Inverse Gaussian Distribution 2957.14 Lognormal Distribution 2967.15 Pareto Distribution 3027.16 Double Exponential Distribution 3047.17 Central chi2 Distribution 3077.18 Student's T Distribution 3107.19 Snedecor's F Distribution 3157.20 Fisher's Z Distribution 3177.22 Rayleigh Distribution 3217.23 Chi-Distribution 3237.24 Maxwell Distribution 3247.25 Summary 3268 Mathematical Expectation 3338.1 Meaning of Expectation 3338.2 Random Variable 3348.3 Expectation of Functions of Random Variables 3468.4 Conditional Expectations 3558.5 Inverse Moments 3618.6 Incomplete Moments 3628.7 Distances as Expected Values 3628.8 Summary 3639 Generating Functions 3739.1 Types of Generating Functions 3739.2 Probability Generating Functions (PGF) 3759.3 Generating Functions for CDF (GFCDF) 3789.4 Generating Functions for Mean Deviation (GFMD) 3799.5 Moment Generating Functions (MGF) 3809.6 Characteristic Functions (ChF) 3849.7 Cumulant Generating Functions (CGF) 3879.8 Factorial Moment Generating Functions (FMGF) 3899.9 Conditional Moment Generating Functions (CMGF) 3909.10 Convergence of Generating Functions 3919.11 Summary 39110 Functions of Random Variables 39510.1 Functions of Random Variables 39510.2 Distribution of Translations 39710.3 Distribution of Constant Multiples 39710.4 Method of Distribution Functions (MoDF) 39810.5 Change of Variable Technique 40110.6 Distribution of Squares 40310.7 Distribution of Square-Roots 40410.8 Distribution of Reciprocals 40610.9 Distribution of Minimum and Maximum 40610.10 Distribution of Trigonometric Functions 40710.11 Distribution of Transcendental Functions 40710.12 Transformations of Normal Variates 41310.13 Summary 41411 Joint Distributions 41711.1 Joint and Conditional Distributions 41711.2 Jacobian of Transformations 42111.3 Polar Transformations 43311.4 Summary 438References 441Index 455