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Table of Contents
Preface to the Second Edition; Preface to the First Edition; Contents; Chapter 1: Overview; 1.1 Outline; References; Further Readings; Information on Software; Chapter 2: Concepts of Probability and Statistics; 2.1 Introduction; 2.2 Random Variables, Probability Density Functions, and Cumulative Distribution Functions; 2.3 Characteristic Functions, Moment Generating Functions and Laplace Transforms; 2.4 Some Commonly Used Probability Density Functions; 2.4.1 Beta Distribution; 2.4.2 Binomial Distribution; 2.4.3 Cauchy Distribution; 2.4.4 Chi-Squared Distribution; 2.4.5 Erlang Distribution
2.4.6 Exponential Distribution2.4.7 F (Fisher-Snedecor) Distribution; 2.4.8 Gamma Distribution; 2.4.9 Generalized Gamma Distribution; 2.4.10 Inverse Gaussian (Wald) Distribution; 2.4.11 Laplace Distribution; 2.4.12 Lognormal Distribution; 2.4.13 Nakagami Distribution; 2.4.14 Non-Central Chi-Squared Distribution; 2.4.15 Normal (Gaussian) Distribution; 2.4.16 Poisson Distribution; 2.4.17 Rayleigh Distribution; 2.4.18 Rectangular or Uniform Distribution; 2.4.19 StudentÂś t Distribution; 2.4.20 Weibull Distribution; 2.5 Joint, Marginal and Conditional Densities
2.6 Expectation, Covariance, Correlation, Independence, and Orthogonality2.7 Central Limit Theorem; 2.8 Transformation of Random Variables; 2.8.1 Derivation of the pdf and CDF of Y=g(X); 2.8.2 Probability Density Function of Z=X+Y; 2.8.3 Joint pdf of Functions of Two or More Random Variables; 2.8.4 Use of CHF to Obtain pdf of Sum of Random Variables; 2.8.5 Some Transformations of Interest in Wireless Communications; 2.9 Some Bivariate Correlated Distributions of Interest in Wireless Communications; 2.9.1 Bivariate Normal pdf; 2.9.2 Bivariate Nakagami pdf; 2.9.3 Bivariate Gamma pdf
2.9.4 Bivariate Generalized Gamma pdf2.9.5 Bivariate Weibull pdf; 2.9.6 Bivariate Rician Distribution; 2.10 Order Statistics; 2.10.1 A Few Special Cases of Order Statistics in Wireless Communications; 2.11 Decision Theory and Error Rates; 2.11.1 Gaussian Case; 2.11.2 Non-Gaussian Case; 2.12 Upper Bounds on the Tail Probability; 2.12.1 Chebyshev Inequality; 2.12.2 Chernoff Bound; 2.13 Stochastic Processes; 2.14 Parameter Estimation and Testing; 2.14.1 Method of Moments; 2.14.2 Maximum Likelihood Estimation; 2.14.3 Comparison of MoM and MLE; 2.14.3.1 Gamma Distribution
2.14.3.2 Generalized Gamma Density2.14.3.3 Generalized K Distribution; 2.14.3.4 Gamma-Lognormal (Shadowed Fading Channel); 2.15 Chi-Square Tests; 2.15.1 Exponential Density; 2.15.2 K Distribution; 2.16 MSE and Chi-Square Test; 2.17 Mixture Densities in Wireless Channel Modeling; 2.18 Receiver Operating Characteristics; 2.19 Laplace and Mellin Transforms; 2.19.1 Laplace Transforms and Sums of Random Variables; 2.19.1.1 Two Exponential Variables; 2.19.1.2 Two Identical Gamma Variable: G(m,a) and G(m,a); 2.19.1.3 Two Non-Identical Gamma Variables (Different Orders): G(m,a) and G(n,a); 2.19.1.4 Two Non-Identical Gamma Variables (Identical Order): G(m,a) and G(m,b).
2.4.6 Exponential Distribution2.4.7 F (Fisher-Snedecor) Distribution; 2.4.8 Gamma Distribution; 2.4.9 Generalized Gamma Distribution; 2.4.10 Inverse Gaussian (Wald) Distribution; 2.4.11 Laplace Distribution; 2.4.12 Lognormal Distribution; 2.4.13 Nakagami Distribution; 2.4.14 Non-Central Chi-Squared Distribution; 2.4.15 Normal (Gaussian) Distribution; 2.4.16 Poisson Distribution; 2.4.17 Rayleigh Distribution; 2.4.18 Rectangular or Uniform Distribution; 2.4.19 StudentÂś t Distribution; 2.4.20 Weibull Distribution; 2.5 Joint, Marginal and Conditional Densities
2.6 Expectation, Covariance, Correlation, Independence, and Orthogonality2.7 Central Limit Theorem; 2.8 Transformation of Random Variables; 2.8.1 Derivation of the pdf and CDF of Y=g(X); 2.8.2 Probability Density Function of Z=X+Y; 2.8.3 Joint pdf of Functions of Two or More Random Variables; 2.8.4 Use of CHF to Obtain pdf of Sum of Random Variables; 2.8.5 Some Transformations of Interest in Wireless Communications; 2.9 Some Bivariate Correlated Distributions of Interest in Wireless Communications; 2.9.1 Bivariate Normal pdf; 2.9.2 Bivariate Nakagami pdf; 2.9.3 Bivariate Gamma pdf
2.9.4 Bivariate Generalized Gamma pdf2.9.5 Bivariate Weibull pdf; 2.9.6 Bivariate Rician Distribution; 2.10 Order Statistics; 2.10.1 A Few Special Cases of Order Statistics in Wireless Communications; 2.11 Decision Theory and Error Rates; 2.11.1 Gaussian Case; 2.11.2 Non-Gaussian Case; 2.12 Upper Bounds on the Tail Probability; 2.12.1 Chebyshev Inequality; 2.12.2 Chernoff Bound; 2.13 Stochastic Processes; 2.14 Parameter Estimation and Testing; 2.14.1 Method of Moments; 2.14.2 Maximum Likelihood Estimation; 2.14.3 Comparison of MoM and MLE; 2.14.3.1 Gamma Distribution
2.14.3.2 Generalized Gamma Density2.14.3.3 Generalized K Distribution; 2.14.3.4 Gamma-Lognormal (Shadowed Fading Channel); 2.15 Chi-Square Tests; 2.15.1 Exponential Density; 2.15.2 K Distribution; 2.16 MSE and Chi-Square Test; 2.17 Mixture Densities in Wireless Channel Modeling; 2.18 Receiver Operating Characteristics; 2.19 Laplace and Mellin Transforms; 2.19.1 Laplace Transforms and Sums of Random Variables; 2.19.1.1 Two Exponential Variables; 2.19.1.2 Two Identical Gamma Variable: G(m,a) and G(m,a); 2.19.1.3 Two Non-Identical Gamma Variables (Different Orders): G(m,a) and G(n,a); 2.19.1.4 Two Non-Identical Gamma Variables (Identical Order): G(m,a) and G(m,b).