Distribution functions and expectations. (2023)

• Record Type: Book
• Further Information: Note: Robert R. Reitano.
• Authors: Reitano, Robert R, 1950-
• Contents: Preface Introduction 1 Distribution and Density Functions l.l Summary of Book II Results l.l.l DistributionFunctionsonJR l.l.2 Distribution Functions on JRn l.2 DecompositionofDistributionFunctionsonJR l.3 DensityFunctionsonJR l.3.l TheLebesgueApproach l.3.2 RiemannApproach l.3.3 Riemann-Stieltjes Framework l.4 Examples of Distribution Functions on JR l.4.l DiscreteDistributionFunctions l.4.2 ContinuousDistributionFunctions l.4.3 MixedDistributionFunctions 2 Transformed Random Variables- 2.l MonotonicTransformations 2.2 SumsofIndependentRandomVariables 2.2.l DistributionFunctionsofSums 2.2.2 Density Functions of Sums 2.3 Ratios of Random Variables 2.3.l Independent Random Variable 2.3.2 Example without Independence 3 Order Statistics 3.l-M -Samples and Order Statistics 3.2-Distribution Functions for kth Order Statistics 3.3-Density Functions for kth Order Statistics 3.4-Joint Distribution of all Order Statistics 3.5-Density Functions on JRn 3.6-Multivariate Density Functions -3.6.l Joint Density of all Order Statistics -3.6.2 Marginal Densities and Distributions -3.6.3 Conditional Densities and Distributions 3.7-The Renyi Representation Theorem 4 EXpectationsofRandomVariables1 4.l General Definitions 4.l.l Is Expectation Well Defined? 4.l.2 Formal Resolution of Well-Definedness 4.2 Moments of Distributions 4.2.l Common Types of Moments 4.2.2 Moment Generating Function 4.2.3 Moments of Sums - Theory 4.2.4 Moments of Sums - Applications 4.2.5 Properties of Moments 4.2.6 Moment Examples-Discrete Distributions 4.2.7 Moment Examples-Continuous Distributions 4.3 Moment Inequalities 4.3.l Chebyshev's Inequality 4.3.2 Jensen's Inequality 4.3.3 Kolmogorov's Inequality 4.3.4 Cauchy-Schwarz Inequality 4.3.5 Holder and Lyapunov Inequalities 4.4 Uniqueness of Moments 4.4.l Applications of Moment Uniqueness 4.5 Weak Convergence and Moment Limits 5 Simulating Samples of RVs - EXamples 5.l Random Samples 5.l.l Discrete Distributions 5.l.2 Simpler Continuous Distributions 5.l.3 Normal and Lognormal Distributions 5.l.4 Student T Distribution 5.2 Ordered Random Samples 5.2.l Direct Approaches 5.2.2 The Renyi Representation 6 Limit Theorems 6.l Introduction 6.2 Weak Convergence of Distributions 6.2.l Student T ⇒ Normal 6.2.2 Poisson Limit Theorem 6.2.3 "Weak Law of Small Numbers" 6.2.4 De Moivre-Laplace Theorem 6.2.5 The Central Limit Theorem l 6.2.6 Smirnov's Theorem on Uniform Order Statistics 6.2.7 A Limit Theorem on General Quantiles 6.2.8 A Limit Theorem on Exponential Order Statistics 6.3 Laws of Large Numbers 6.3.l Tail Events and Kolmogorov's 0-l Law 6.3.2 Weak Laws of Large Numbers 6.3.3 Strong Laws of Large Numbers 6.3.4 A Limit Theorem in EVT 6.4 Convergence of Empirical Distributions 6.4.l Definition and Basic Properties 6.4.2 The Glivenko-Cantelli Theorem 6.4.3 Distributional Estimates for Dn (s ) 7 Estimating Tail Events 2 7.l Large Deviation Theory 2 7.l.l Chernoff Bound 7.l.2 Cramer-Chernoff Theorem 7.2 Extreme Value Theory 2 7.2.l Fisher-Tippett-Gnedenko theorem 7.2.2 The Hill Estimator, 1 > 0 7.2.3 F E D (G, ) is Asymptotically Pareto for 1 > 0 7.2.4 F E D (G, ), 1 > 0, then 1 H � 1 7.2.5 F E D (G, ), 1 > 0, then 1 H -1 1 7.2.6 Asymptotic Normality of the Hill Estimator 7.2.7 The Pickands-Balkema-de Haan Theorem: 1 > 0 References
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2023
• Extent: 1 online resource (250 pages)
• Subjects: 332.015195; Finance -- Mathematical models; Distribution (Probability theory)
• Languages: English
• ISBNs: 9781000934540
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.