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Data Analytics: Handbook of Formulas and Techniques [Kõva köide]

(Air Force Institute of Technology, Dayton, Ohio, USA)
  • Formaat: Hardback, 246 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 20 Tables, black and white; 32 Line drawings, black and white; 1 Halftones, black and white; 33 Illustrations, black and white
  • Sari: Systems Innovation Book Series
  • Ilmumisaeg: 23-Dec-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367537419
  • ISBN-13: 9780367537418
Teised raamatud teemal:
Data Analytics: Handbook of Formulas and TechniquesSuurem pilt
  • Formaat: Hardback, 246 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 20 Tables, black and white; 32 Line drawings, black and white; 1 Halftones, black and white; 33 Illustrations, black and white
  • Sari: Systems Innovation Book Series
  • Ilmumisaeg: 23-Dec-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367537419
  • ISBN-13: 9780367537418
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367537418.html
Märksõnad:

Good data analytics is the basis for effective decisions. Whoever has the data, has the ability to extract information promptly and effectively to make pertinent decisions. The premise of this handbook is to empower users and tool developers with the appropriate collection of formulas and techniques for data analytics and to serve as a quick reference to keep pertinent formulas within fingertip reach of readers.

This handbook includes formulas that will appeal to mathematically inclined readers. It discusses how to use data analytics to improve decision-making and is ideal for those new to using data analytics to show how to expand their usage horizon. It provides quantitative techniques for modeling pandemics, such as COVID-19. It also adds to the suite of mathematical tools for emerging technical areas.

This handbook is a handy reference for researchers, practitioners, educators, and students in areas such as industrial engineering, production engineering, project management, civil engineering, mechanical engineering, technology management, and business management worldwide.

Preface xxi
Acknowledgments xxiii
Author xxv
Chapter 1 Essentials of Data Analytics
1(28)
Introduction to COVID-19 Data Analytics
1(1)
Systems View of Data Analytics
2(1)
Global Growth of Data Analytics
2(1)
Background in Predictive Analytics
3(2)
Data Modeling Approaches
5(1)
Data Fanaticism
6(1)
Data and Measurements for Data Analytics
7(9)
What Is Measurement?
7(1)
Data Measurement Systems
8(3)
Fundamental Scientific Equations
11(1)
Einstein's Equation
11(1)
Einstein's Field Equation
11(1)
Heisenberg's Uncertainty Principle
12(1)
Schrodinger Equation
12(1)
Dirac Equation
12(1)
Maxwell's Equations
13(1)
Boltzmann's Equation for Entropy
13(1)
Planck--Einstein Equation
13(1)
Planck's Blackbody Radiation Formula
14(1)
Hawking Equation for Black Hole Temperature
14(1)
Navier--Stokes Equation for a Fluid
14(1)
Lagrangian for Quantum Chromodynamics
14(1)
Bardeen--Cooper--Schrieffer Equation for Superconductivity
14(1)
Josephson Effect
15(1)
Fermat's Last Theorem
15(1)
Methods for Data Measurement and Comparison
16(1)
Direct Comparison
16(1)
Indirect Comparison
17(1)
Data Measurement Scales
17(2)
Nominal Scale of Measurement
18(1)
Ordinal Scale of Measurement
18(1)
Interval Scale of Measurement
18(1)
Ratio Scale Measurement
18(1)
Reference Units of Measurements
19(1)
Common Constants
20(1)
Numeric Data Representation
20(1)
The Language of Data Analytics
21(1)
Quick Reference for Mathematical Equations
21(7)
Reference
28(1)
Chapter 2 Empirical Model Building
29(22)
Introduction to the Model Environment
29(1)
State-Space Modeling
30(2)
Calculus Reference for Data Analytics
32(1)
Integration Rules
33(1)
Solving Integrals with Variable Substitution
34(1)
Riemann Integral
34(1)
Integration by Parts
34(2)
Compound Functions Where the Inner Function Is αx
34(1)
Integration by Parts
35(1)
Systems Modeling for Data Analytics
36(3)
Triple C Questions
39(1)
Communication
40(5)
Cooperation
45(2)
Coordination
47(1)
Conflict Resolution in Data Analytics
47(2)
References
49(2)
Chapter 3 Data Visualization Methods
51(18)
Introduction to Data Visualization
51(1)
Case Example of "Covidvisualizer" Website
51(1)
Dynamism and Volatility of Data
52(1)
Data Determination and Collection
53(10)
Choosing the Data
53(1)
Collecting the Data
53(1)
Relevance Check
54(1)
Limit Check
54(1)
Critical Value
54(1)
Coding the Data
54(1)
Processing the Data
54(1)
Control Total
54(1)
Consistency Check
55(1)
Scales of Measurement
55(1)
Using the Information
55(2)
Data Exploitation
57(1)
Raw Data
57(1)
Total Revenue
58(1)
Average Revenue
59(2)
Median Revenue
61(1)
Quartiles and Percentiles
62(1)
The Mode
63(1)
Range of Revenue
63(1)
Average Deviation
63(1)
Sample Variance
64(1)
Standard Deviation
65(4)
Chapter 4 Basic Mathematical Calculations for Data Analytics
69(60)
Introduction to Calculation for Data Analytics
69(1)
Quadratic Equation
69(5)
Overall Mean
70(1)
Chebyshev's Theorem
70(1)
Permutations
70(1)
Combinations
70(1)
Failure
71(1)
Probability Distribution
71(1)
Probability
71(1)
Distribution Function
71(1)
Expected Value
72(1)
Variance
72(1)
Binomial Distribution
73(1)
Poisson Distribution
73(1)
Mean of a Binomial Distribution
73(1)
Variance
73(1)
Normal Distribution
73(1)
Cumulative Distribution Function
73(1)
Population Mean
73(1)
Standard Error of the Mean
74(1)
T-Distribution
74(1)
Chi-Squared Distribution
74(1)
Definition of Set and Notation
74(1)
Set Terms and Symbols
75(1)
Venn Diagrams
75(3)
Operations on Sets
76(1)
De Morgan's Laws
76(1)
Probability Terminology
77(1)
Basic Probability Principles
77(1)
Random Variable
77(1)
Mean Value x or Expected Value μ
78(1)
Series Expansions
78(3)
Mathematical Signs and Symbols
81(2)
Greek Alphabet
83(1)
Algebra
83(8)
Laws of Algebraic Operations
83(1)
Special Products and Factors
83(2)
Powers and Roots
85(1)
Proportion
85(1)
Arithmetic Mean of n Quantities A
86(1)
Geometric Mean of n Quantities G
86(1)
Harmonic Mean of n Quantities H
86(1)
Generalized Mean
86(1)
Solution of Quadratic Equations
87(1)
Solution of Cubic Equations
87(1)
Trigonometric Solution of the Cubic Equation
88(1)
Solution of Quadratic Equations
89(1)
Partial Fractions
89(1)
Non-repeated Linear Factors
89(1)
Repeated Linear Factors
90(1)
General Terms
90(1)
Repeated Linear Factors
91(1)
Factors of Higher Degree
91(1)
Geometry
91(11)
Triangles
91(1)
Right Triangle
92(1)
Equilateral Triangle
92(1)
General Triangle
92(1)
Menelaus's Theorem
93(1)
Ceva's Theorem
93(1)
Quadrilaterals
93(1)
Rectangle
93(1)
Parallelogram
94(1)
Rhombus
94(1)
Trapezoid
94(1)
General Quadrilateral
94(1)
Regular Polygon of n Sides Each of Length b
95(1)
Regular Polygon of n Sides Inscribed in a Circle of Radius r
95(1)
Regular Polygon of n Sides Circumscribing a Circle of Radius r
95(1)
Cyclic Quadrilateral
95(1)
Prolemy's Theorem
96(1)
Cyclic-Inscriptable Quadrilateral
96(1)
Planar Areas by Approximation
97(1)
Trapezoidal Rule
97(1)
Durand's Rule
97(1)
Simpson's Rule (n even)
97(1)
Weddle's Rule (n = 6)
98(1)
Solids Bounded by Planes
98(1)
Cube
98(1)
Rectangular Parallelepiped (or Box)
98(1)
Prism
98(1)
Pyramid
98(1)
Prismatoid
99(1)
Regular Polyhedra
99(1)
Sphere of Radius r
100(1)
Right Circular Cylinder of Radius r and Height h
100(1)
Circular Cylinder of Radius r and Slant Height
100(1)
Cylinder of Cross-Sectional Area A and Slant Height
100(1)
Right Circular Cone of Radius r and Height h
101(1)
Spherical Cap of Radius r and Height h
101(1)
Frustum of Right Circular Cone of Radii a, b and Height h
101(1)
Zone and Segment of Two Bases
101(1)
Lune
101(1)
Spherical Sector
101(1)
Spherical Triangle and Polygon
101(1)
Spheroids
102(1)
Ellipsoid
102(1)
Oblate Spheroid
102(1)
Prolate Spheroid
102(1)
Circular Torus
102(1)
Formulas from Plane Analytic Geometry
102(25)
Distance d between Two Points
102(1)
Slope m of Line Joining Two Points
103(1)
Equation of Line Joining Two Points
103(1)
Equation of Line in Terms of x Intercept a ≠ 0 and y intercept b ≠ 0
103(1)
Normal Form for Equation of Line
103(1)
General Equation of Line
103(1)
Distance from Point (x1, y1) to Line Ax + By + C = 0
103(1)
Angle Φ between Two Lines Having Slopes m1 and m2
103(1)
Area of Triangle with Verticles
104(1)
Transformation of Coordinates Involving Pure Translation
104(1)
Transformation of Coordinates Involving Pure Rotation
104(1)
Transformation of Coordinates Involving Translation and Rotation
104(1)
Polar Coordinates (r, θ)
105(1)
Plane Curves
105(1)
Catenary, Hyperbolic Cosine
105(1)
Cardioid
105(1)
Circle
105(1)
Cassinian Curves
105(1)
Cotangent Curve
106(1)
Cubical Parabola
106(1)
Cosecant Curve
106(1)
Cosine Curve
106(1)
Ellipse
106(1)
Gamma Function
106(1)
Hyperbolic Functions
106(1)
Inverse Cosine Curve
107(1)
Inverse Sine Curve
107(1)
Inverse Tangent Curve
107(1)
Logarithmic Curve
107(1)
Parabola
107(1)
Cubical Parabola
107(1)
Tangent Curve
107(1)
Ellipsoid
107(1)
Elliptic Cone
107(1)
Elliptic Cylinder
107(1)
Hyperboloid of One Sheet
108(1)
Elliptic Paraboloid
108(1)
Hyperboloid of Two Sheets
108(1)
Hyperbolic Paraboloid
108(1)
Sphere
108(1)
Distance d between Two Points
108(1)
Equations of Line Joining P1(x1, y1, Z1) and P2(x2, y2, z2) in Standard Form
108(1)
Equations of Line Joining P1(x1, y1, Z1) and P2(x2, y2, z2) in Parametric Form
108(1)
Angle φ between Two Lines with Direction Cosines l1, m1, n1 and l2, m2, n2
108(1)
General Equation of a Plane
109(1)
Equation of Plane Passing through Points
109(1)
Equation of Plane in Intercept Form
109(1)
Equations of Line through (x0, x0, z0) and Perpendicular to Plane
109(1)
Distance from Point [ x, y, z) to Plane Ax + By + D = 0
109(1)
Normal form for Equation of Plane
109(1)
Transformation of Coordinates Involving Pure Translation
110(1)
Transformation of Coordinates Involving Pure Rotation
110(1)
Transformation of Coordinates Involving Translation and Rotation
110(1)
Cylindrical Coordinates (r, θ, z)
111(1)
Spherical Coordinates (r, θ, φ)
111(1)
Logarithmic Identities
112(1)
Special Values
112(1)
Logarithms to General Base
112(1)
Series Expansions
113(1)
Limiting Values
113(1)
Inequalities
113(1)
Continued Fractions
114(1)
Polynomial Approximations
114(1)
Fundamental Properties
115(1)
Definition of General Powers
116(1)
Logarithmic and Exponential Functions
116(1)
Polynomial Approximations
117(8)
Slopes
125(1)
Trigonometric Ratios
125(2)
Sine Law
127(1)
Cosine Law
127(1)
Algebra
127(2)
Expanding
127(1)
Factoring
127(1)
Roots of Quadratic
128(1)
Law of Exponents
128(1)
Logarithms
128(1)
Chapter 5 Statistical Methods for Data Analytics
129(56)
Introduction
129(1)
Discrete Distributions
129(5)
Bernoulli Distribution
129(1)
Beta Binomial Distribution
129(3)
Beta Pascal Distribution
132(1)
Binomial Distribution
132(1)
Discrete Weibull Distribution
132(1)
Geometric Distribution
132(1)
Hypergeometric Distribution
133(1)
Negative Binomial Distribution
133(1)
Poisson Distribution
134(1)
Rectangular (Discrete Uniform) Distribution
134(1)
Continuous Distributions
134(8)
Arcsin Distribution
134(1)
Beta Distribution
135(1)
Cauchy Distribution
135(1)
Chi Distribution
135(1)
Chi-Square Distribution
135(1)
Erlang Distribution
136(1)
Exponential Distribution
136(1)
Extreme-Value Distribution
136(1)
F Distribution
136(1)
Gamma Distribution
137(1)
Half-Normal Distribution
137(1)
Laplace (Double Exponential) Distribution
138(1)
Logistic Distribution
138(1)
Lognormal Distribution
138(1)
Noncentral Chi-Square Distribution
139(1)
Noncentral F Distribution
139(1)
Noncentral t Distribution
139(1)
Normal Distribution
140(1)
Pareto Distribution
140(1)
Rayleigh Distribution
140(1)
T Distribution
141(1)
Triangular Distribution
141(1)
Uniform Distribution
142(1)
Weibull Distribution
142(1)
Distribution Parameters
142(2)
Average
142(1)
Variance
142(1)
Standard Deviation
143(1)
Standard Error
143(1)
Skewness
143(1)
Standardized Skewness
143(1)
Kurtosis
143(1)
Standardized Kurtosis
143(1)
Weighted Average
143(1)
Estimation and Testing
144(2)
100(1 -- α)% Confidence Interval for Mean
144(1)
100(1 -- α)% Confidence Interval for Variance
144(1)
100(1 -- α)% Confidence Interval for Difference in Means
144(1)
Equal Variance
144(1)
Unequal Variance
144(1)
100(1 -- α)% Confidence Interval for Ratio of Variances
145(1)
Normal Probability Plot
145(1)
Comparison of Poisson Rates
145(1)
Distribution Functions and Parameter Estimation
146(5)
Bernoulli
146(1)
Binomial
146(1)
Discrete Uniform
146(1)
Geometric
146(1)
Negative Binomial
146(1)
Poisson
146(1)
Beta
146(1)
Chi-Square
147(1)
Erlang
147(1)
Exponential
147(1)
F
147(1)
Gamma
147(1)
Lognormal
148(1)
System Displays
148(1)
Normal
148(1)
Student's t
148(1)
Triangular
148(1)
Uniform
149(1)
Weibull
149(1)
Chi-Square Test for Distribution Fitting
149(1)
Kolmogorov-Smirnov Test
149(1)
Anova (Analysis of Variance)
150(1)
Notations
150(1)
Standard Error (Internal)
151(1)
Standard Error (Pooled)
151(1)
Interval Estimates
151(1)
Tukey Interval
151(1)
Scheffe Interval
151(1)
Cochran C-Test
151(1)
Bartlett Test
152(1)
Hartley's Test
152(1)
Kruskal--Wallis Test
152(1)
Freidman Test
153(1)
Regression
154(8)
Notations
154(1)
Regression Statistics
154(1)
Predictions
155(1)
Nonlinear Regression
156(1)
Ridge Regression
157(1)
Quality Control
157(1)
Subgroup Statistics
157(1)
X-Bar Charts
158(1)
Capability Ratios
159(1)
R Charts
159(1)
S Charts
160(1)
C Charts
160(1)
U Charts
160(1)
P Charts
160(1)
NP Charts
161(1)
CuSum Chart for the Mean
161(1)
Multivariate Control Charts
162(1)
Time Series Analysis
162(2)
Notations
162(1)
Autocorrelation at Lag k
162(1)
Partial Autocorrelation at Lag k
163(1)
Cross-Correlation at Lag k
163(1)
Box-Cox
163(1)
Periodogram (Computed Using Fast Fourier Transform)
164(1)
Categorical Analysis
164(6)
Notations
164(1)
Totals
164(1)
Chi-Square
165(1)
Fisher's Exact Test
165(1)
Lambda
165(1)
Uncertainty Coefficient
165(1)
Somer's D
166(1)
Eta
167(1)
Contingency Coefficient
167(1)
Cramer's V
168(1)
Conditional Gamma
168(1)
Pearson's r
168(1)
Kendall's Tau b
168(1)
Tau C
168(1)
Probability Terminology
168(1)
Basic Probability Principles
169(1)
Random Variable
169(1)
Mean Value x or Expected Value μ
169(1)
Discrete Distribution Formulas
170(13)
Bernoulli Distribution
170(1)
Beta Binomial Distribution
170(1)
Beta Pascal Distribution
171(1)
Binomial Distribution
171(1)
Discrete Weibull Distribution
171(1)
Geometric Distribution
171(1)
Hypergeometric Distribution
171(1)
Negative Binomial Distribution
172(1)
Poisson Distribution
172(1)
Rectangular (Discrete Uniform) Distribution
173(1)
Continuous Distribution Formulas
173(1)
Arcsin Distribution
173(1)
Beta Distribution
173(1)
Cauchy Distribution
174(1)
Chi Distribution
174(1)
Chi-Square Distribution
174(1)
Erlang Distribution
174(1)
Exponential Distribution
175(1)
Extreme-Value Distribution
175(1)
F Distribution
175(1)
Gamma Distribution
176(1)
Half-Normal Distribution
176(1)
Laplace (Double Exponential) Distribution
176(1)
Logistic Distribution
177(1)
Lognormal Distribution
177(1)
Noncentral Chi-Square Distribution
177(1)
Noncentral F Distribution
178(1)
Noncentral t Distribution
178(1)
Normal Distribution
178(1)
Pareto Distribution
179(1)
Rayleigh Distribution
179(1)
T Distribution
179(1)
Triangular Distribution
180(1)
Uniform Distribution
180(1)
Weibull Distribution
180(1)
Variate Generation Techniques
181(2)
Reference
183(2)
Chapter 6 Descriptive Statistics for Data Presentation
185(26)
Introduction
185(3)
Sample Average
185(1)
Sample Variance
185(1)
Sample Standard Deviation
186(1)
Sample Standard Error of the Mean
187(1)
Skewness
187(1)
Standardized Skewness
188(1)
Kurtosis
188(1)
Standardized Kurtosis
188(1)
Weighted Average
188(1)
Estimation and Testing
188(2)
100(1 -- α)% Confidence Interval for Mean
188(1)
100(1 -- α)% Confidence Interval for Variance
188(1)
100(1 -- α)% Confidence Interval for Difference in Means
188(1)
For Equal Variance
188(1)
For Unequal Variance
189(1)
100(1 -- α)% Confidence Interval for Ratio of Variances
189(1)
Normal Probability Plot
189(1)
Comparison of Poisson Rates
190(1)
Distribution functions and Parameter Estimation
190(5)
Bernoulli Distribution
190(1)
Binomial Distribution
190(1)
Discrete Uniform Distribution
190(1)
Geometric Distribution
190(1)
Negative Binomial Distribution
191(1)
Poisson Distribution
191(1)
Beta Distribution
191(1)
Chi-Square Distribution
191(1)
Erlang Distribution
191(1)
Exponential Distribution
192(1)
F Distribution
192(1)
Gamma Distribution
192(1)
Lognormal Distribution
192(1)
Normal Distribution
193(1)
Student's t
193(1)
Triangular Distribution
193(1)
Uniform Distribution
193(1)
Weibull Distribution
193(1)
Chi-Square Test for Distribution Fitting
194(1)
Kolmogorov-Smirnov Test
194(1)
ANOVA (Analysis of Variance)
194(1)
Notations
194(1)
Standard Error
195(1)
Interval Estimates
195(1)
Tukey Interval
195(1)
Scheffe Interval
196(1)
Cochran C-test
196(1)
Bartlett Test
196(1)
Hartley's Test
196(1)
Kruskal--Wallis Test
197(1)
Freidman Test
197(1)
Regression
198(5)
Notations
198(1)
Statistical Quality Control
199(1)
Subgroup Statistics
199(1)
X-Bar Charts
199(1)
Capability Ratios
200(1)
R Charts
201(1)
S Charts
201(1)
C Charts
201(1)
U Charts
201(1)
P Charts
201(1)
NP Charts
202(1)
CuSum Chart for the Mean
202(1)
Time Series Analysis
203(2)
Notations
203(1)
Autocorrelation at Lag k
203(1)
Partial Autocorrelation at Lag k
203(1)
Cross-Correlation at Lag k
203(1)
Box-Cox Computation
204(1)
Periodogram (Computed Using Fast Fourier Transform)
204(1)
Categorical Analysis
205(6)
Notations
205(1)
Totals
205(1)
Chi-Square
205(1)
Lambda
205(1)
Uncertainty Coefficient
206(1)
Somer's D Measure
206(1)
Eta
207(1)
Contingency Coefficient
208(1)
Cramer's V Measure
208(1)
Conditional Gamma
208(1)
Pearson's r Measure
208(1)
Kendall's Tau b Measure
208(1)
Tau C Measure
209(1)
Overall Mean
209(1)
Chebyshev's Theorem
209(1)
Permutation
209(1)
Combination
209(1)
Failure
209(2)
Chapter 7 Data Analytics Tools for Understanding Random Field Regression Models
211(22)
Introduction
211(1)
RFR Models
212(2)
Two Examples
214(1)
Bayesian Regression Models and Random Fields
214(1)
Data Analysis: Finding the Associated Regression Model
215(8)
Relating Eigenvectors to Regression Functions
223(2)
Some Special Random Field Models
225(1)
Gaussian Covariance as Damped Polynomial Regression
225(2)
Trigonometric Regression and Spline Covariance
227(1)
Discussion
228(1)
References
229(4)
Chapter 8 Application of DEJI Systems Model to Data Integration
233(10)
Introduction to Data Integration
233(1)
Leveraging the Input-Control-Output-Mechanism Model
234(1)
Data Types and Fidelity
235(1)
Data Collection and Sanitization
236(2)
DEJI Systems Model for Data Quality
238(1)
Data Value Model
239(2)
Data Quality Control
241(1)
References
242(1)
Index 243
Adedeji B. Badiru is a professor of systems engineering at the Graduate School of Engineering and Management at the Air Force Institute of Technology. He was previously Professor and Department Head of Industrial Engineering at the University of Tennessee, and Professor of Industrial Engineering at the University of Oklahoma. He is a registered professional engineer (PE), a certified Project Management Professional (PMP), and a Fellow of the Institute of Industrial & Systems Engineers. He is the author of over 30 books, 34 book chapters, and 80 technical journal articles. He is a member of several professional associations and scholastic honor societies.