Continuous Distributions in Engineering and the Applied Sciences: Part I

List of Figures
List of Tables
Preface
Glossary of Terms
Continuous Random Variables
	Introduction
		Continuous Models
		Standard Distributions
		Tail Areas
	Moments and Cumulants
	Size-Biased Distributions
	Location-and-Scale Distributions
	Truncated Distributions
	Transmuted Distributions
	Other Extensions
	Mean Deviation of Continuous Distributions
		New Measures of Dispersion
		A New Family of Distributions
	Random Numbers
	Data Outliers
	Summary
Rectangular Distribution
	Introduction
		Alternate Representations
	Related Distributions
	Properties of Rectangular Distribution
		Moments and Generating Functions
		Truncated Uniform Distributions
	Applications
	Triangular Distributions
	Summary
Exponential Distribution
	Introduction
		Alternate Representations
	Relation to Other Distributions
	Properties of Exponential Distribution
		Moments and Generating Functions
		Additivity Property
		Memory-Less Property
	Random Numbers
	Fitting
	Generalizations
	Applications
		Hydraulics
		Tensile Strengths
	Summary
Beta Distribution
	Introduction
		Alternate Representations
	Relation to Other Distributions
	Properties of Type-I Beta Distribution
		Moments and Generating Functions of Type-I Beta
	Type-II Beta Distribution
		Relation to Other Distributions
	Properties of Type-II Beta Distribution
		Moments and Generating Functions of Type-II Beta
	Size-Biased Beta Distributions
	The Incomplete Beta Function
		Tail Areas Using IBF
		Random Numbers
		Fitting
	General Beta Distribution
		Additivity Property
	Applications
		Civil Engineering
		Geotechnical Engineering
		Beta Distribution in Control Charts
		Beta Distribution in PERT
		Confidence Intervals for Binomial Proportions
		Mineralogy
	Summary
Arcsine Distribution
	Introduction
		Alternate Representations
		Relation to Other Distributions
	Properties of Arcsine Distribution
		Moments of Arcsine Distribution
		Tail Areas
	Generalized Arcsine Distributions
		Transmuted Arcsine Distributions
		Weighted Arcsine Distributions
	Applications
		Arcsine Transforms
		Statistical Physics
		Random Walks
	Summary
Gamma Distribution
	Introduction
	Alternate Representations
	Relation to Other Distributions
	Properties of Gamma Distribution
		Additivity Property
		Moments and Generating Functions
	Tail Areas
		Incomplete Gamma Function (IGF)
		Fitting
	General Gamma Distributions
		Truncated Gamma Distributions
	Applications
		Metallurgy
		Reliability
	Summary
Cosine Distribution
	Introduction
	Alternate Representations
	Properties of Cosine Distribution
		Mean and Variance
		Tail Areas
	Truncated Cosine Distributions
		Size-Biased Cosine Distribution
		Transmuted Cosine Distribution
	Special Cosine Distributions
	Applications
		Digital Signal Processing
		Path Planning in Robotics
		Antenna Design
	Summary
Normal Distribution
	Introduction
		Alternate Representations
	Relation to Other Distributions
	Properties of Normal Distribution
		Moments and Generating Functions
		Transformations to Normality
		Tail Areas
		Additivity Property
	Special Normal Distributions
		Truncated Normal Distribution
	Skew-Normal Distribution
		Properties of SND
		The MGF of SND
		Random Samples
		Fitting SND
		Extensions of SND
	Lognormal Distribution
		Alternate Representations
		Properties of Lognormal Distribution
		Moments
		Generating Functions
		Partial Expectation of Lognormal Distribution
		Fitting Lognormal Distribution
	Applications
		Process Control
		Classification
	Summary
Cauchy Distribution
	Introduction
		Alternate Representations
	Properties of Cauchy Distribution
	Relation with Other Distributions
		Functions of Cauchy Variates
		Parameter Estimation
		Tail Areas
	Special Cauchy Distributions
		Truncated Cauchy Distribution
		Log-Cauchy Distribution
		Half-Cauchy Distribution
		Skew-Cauchy Distribution
		Beta-Cauchy Distribution
	Applications
		Thermodynamics
		Carbon Nanotube Strain Sensing
		Biology
	Summary
Bibliography
Authors' Biographies
Index
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