Discrete Distributions in Engineering and the Applied Sciences

List of Figures
List of Tables
Glossary
Discrete Random Variables
	Introduction
		Discrete Models
		Uses of Discrete Probabilistic Models
	Discrete Random Variables
	Conditional Models
	Linear Combination of Random Variables
		Random Sums of Random Variables
		Mixed Random Variables
		Displaced Random Variables
	Domain of a Random Variable
	CDF and SF
		Properties of CDF
	Binomial Theorem
		Recurrence Relation for Binomial Coefficients
		Distributions Obtainable from Binomial Theorem
	Mean Deviation of Discrete Distributions
		New Measures of Variability
		A New Family of Distributions
	Truncated Models
	Zero-Inflated Distributions
	Hurdle Models
	Power Series Distributions
	Summary
Binomial Distribution
	Introduction
		Bernoulli Trials
		``Success\'\' Demystified
		Spatial Processes
		Dichotomization Using Cutoff
	Bernoulli Distribution
		Basic Properties of Bernoulli Distribution
		Related Distributions
		Random Numbers
	Binomial Distribution
		Dependent Trials
	Properties of Binomial Distribution
		Moments
		Moment Recurrences
		Additivity Property
		MD of Binomial Distribution
		New Distribution from MD
		Tests of Hypothesis
		Binomial Confidence Intervals
	Generating Functions
		Probability Generating Functions
		Variance Generating Function (VGF)
	Algorithm for Computing Binomial Distribution
		Tail Probabilities
		Approximations
	Limiting Form of Binomial Distribution
	Special Binomial Distributions
		Distribution of U = |X-Y|/2
		Truncated Binomial Distributions
		Inflated Binomial Distributions
		Log-Binomial Distribution
	Applications
		Microbiology
		Epidemiology
		Genetics
		Reliability
		K-out-of-n System Operation
		K-out-of-n Detection
		Ensemble Methods
		SQC
		Electronics
	Summary
Discrete Uniform Distribution
	Introduction
	Discrete Uniform Distribution
		Mean and Variance
	Properties of Discrete Uniform Distribution
		Special Symmetry
	Relation to Other Distributions
	Applications
		Sampling
		Random Numbers
	Summary
Geometric Distribution
	Derivation
		Alternate Forms
	Relation to Other Distributions
	Properties of Geometric Distribution
		CDF and SF
		Tail Probabilities
		Distribution of Extremes
		Memory-Less Property
		Moments and Generating Functions
	Special Geometric Distributions
		Arithmetico-Geometric Distribution
		Log-Geometric Distributions
		Truncated Geometric Distributions
		Zero-Inflated Geometric Distribution
	Random Samples
	Applications
		Manufacturing
		Machine Failures
		Medical Imaging
		Transportation
	Summary
Negative Binomial Distribution
	Derivation
		Alternate Forms
	Relation to Other Distributions
	Properties of NBINO(k, p)
		MGF of Negative Binomial Distribution
		Moments of Negative Binomial Distribution
		Variance Generating Function
		Factorial Moments
	Poisson Approximation
		Derivation Using PGF
	Moment Recurrence
	Tail Probabilities
	Truncated Negative Binomial Distributions
		Zero-Inflated Negative Binomial (ZINB) Models
	Generalizations
	Applications
		Power Restoration Modeling
		Capture-Mark-Recapture Model
		Medical Sciences
	Summary
Poisson Distribution
	Introduction
		Importance of Counts
	Probability Mass Function
	Dilution Techniques
	Moment Approximation
	Derivation of Poisson Law
	Properties of Poisson Distribution
		Moments and MGF
		Factorial Moments
		Moment Generating Function
		Additivity Property
	Relation to Other Distributions
	Algorithms for Poisson Distribution
	Approximations
	Generalized Poisson Distributions
		Intervened Poisson Distribution (IPD)
		Spinned Poisson Distribution (SPD)
	Poisson Process
	Fitting a Poisson Distribution
	Truncated Poisson Distribution
	Zero-Inflated Poisson Distribution
	Double Poisson Distribution
	Applications
		Healthcare
		Electronics
		Poisson Regression
		Management Sciences
		Quantum Cryptography
		Poisson Heterogeneity Test
	Summary
Hypergeometric Distribution
	Introduction
	Alternate Forms
	Relation to Other Distributions
	Properties of Hypergeometric Distribution
		Factorial Moments of Hypergeometric Distribution
		Mean and Variance of Hypergeometric Distribution
		Generating Functions
		Mean Deviation
	Truncated Hypergeometric Distributions
		Approximations for Hypergeometric Distribution
	Applications
		Hypergeometric Tests
		Fisher\'s Exact Test
		Median Test
		Runs Test
		Acceptance Sampling
		The CMR Model
		Line-Transect Model
		Highway Engineering
		Medical Sciences
		Bioinformatics
	Summary
Negative Hypergeometric Distribution
	Derivation
		Dual NHGD
	Alternate Forms
		Relation to Other Distributions
	Properties of NHGD
		Generating Functions
		Mean and Variance
		Factorial Moments
		Beta-Binomial Distribution
		Mean and Variance
		Mean Deviation
	Truncated NHGD
	Applications
		Computer Games
		CMR Estimation
		Industrial Quality Control
	Summary
Logarithmic Series Distribution
	Introduction
		Alternate Forms
		Relation to Other Distributions
	Properties of Logarithmic Distribution
		Mean and Variance
		Factorial Moments
		CDF and SF
		Generating Functions
	Zero-Inflated Logarithmic Distribution
	Lagrangian Logarithmic Distribution
	Applications
		Scientific Research
		Ecology
		Finance
	Summary
Multinomial Distribution
	Introduction
		Alternate Forms
	Relation to Other Distributions
	Properties of Multinomial Distribution
		Marginal Distributions
		Conditional Distributions
		Generating Functions
		Moments and Cumulants
	Applications
		Contingency Tables
		Genomics
		Finance
		Reliability
	Summary
Bibliography
Authors\' Biographies
Index
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