Examples and Problems in Mathematical Statistics

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Detalles Bibliográficos
Autor principal: Zacks, Shelemyahu
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1.6.4 Quantiles of Distributions
  • 1.6.5 Transformations
  • 1.7 JOINT DISTRIBUTIONS, CONDITIONAL DISTRIBUTIONS AND INDEPENDENCE
  • 1.7.1 Joint Distributions
  • 1.7.2 Conditional Expectations: General Definition
  • 1.7.3 Independence
  • 1.8 MOMENTS AND RELATED FUNCTIONALS
  • 1.9 MODES OF CONVERGENCE
  • 1.10 WEAK CONVERGENCE
  • 1.11 LAWS OF LARGE NUMBERS
  • 1.11.1 The Weak Law of Large Numbers (WLLN)
  • 1.11.2 The Strong Law of Large Numbers (SLLN)
  • 1.12 CENTRAL LIMIT THEOREM
  • 1.13 MISCELLANEOUS RESULTS
  • 1.13.1 Law of the Iterated Logarithm
  • 1.13.2 Uniform Integrability
  • 1.13.3 Inequalities
  • 1.13.4 The Delta Method
  • 1.13.5 The Symbols op and Op
  • 1.13.6 The Empirical Distribution and Sample Quantiles
  • PART II: EXAMPLES
  • PART III: PROBLEMS
  • PART IV: SOLUTIONS TO SELECTED PROBLEMS
  • 2 Statistical Distributions
  • PART I: THEORY
  • 2.1 INTRODUCTORY REMARKS
  • 2.2 FAMILIES OF DISCRETE DISTRIBUTIONS
  • 2.2.1 Binomial Distributions
  • 2.2.2 Hypergeometric Distributions
  • 2.2.3 Poisson Distributions
  • 2.2.4 Geometric, Pascal, and Negative Binomial Distributions
  • 2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS
  • 2.3.1 Rectangular Distributions
  • 2.3.2 Beta Distributions
  • 2.3.3 Gamma Distributions
  • 2.3.4 Weibull and Extreme Value Distributions
  • 2.3.5 Normal Distributions
  • 2.3.6 Normal Approximations
  • 2.4 TRANSFORMATIONS
  • 2.4.1 One-to-One Transformations of Several Variables
  • 2.4.2 Distribution of Sums
  • 2.4.3 Distribution of Ratios
  • 2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS
  • 2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS
  • 2.6.1 The Multinomial Distribution
  • 2.6.2 Multivariate Negative Binomial
  • 2.6.3 Multivariate Hypergeometric Distributions
  • 2.7 MULTINORMAL DISTRIBUTIONS
  • 2.7.1 Basic Theory
  • 2.7.2 Distribution of Subvectors and Distributions of Linear Forms
  • 2.7.3 Independence of Linear Forms
  • 2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES
  • 2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES
  • 2.10 THE ORDER STATISTICS
  • 2.11 t-DISTRIBUTIONS
  • 2.12 F-DISTRIBUTIONS
  • 2.13 THE DISTRIBUTION OF THE SAMPLE CORRELATION
  • 2.14 EXPONENTIAL TYPE FAMILIES
  • 2.15 APPROXIMATING THE DISTRIBUTION OF THE SAMPLE MEAN: EDGEWORTH AND SADDLEPOINT APPROXIMATIONS
  • 2.15.1 Edgeworth Expansion
  • 2.15.2 Saddlepoint Approximation
  • PART II: EXAMPLES

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