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Continuous Bivariate Distributions

:	N Balakrishnan, Chin-Diew Lai
:	Continuous Bivariate Distributions
:	Springer-Verlag
:	9780387096148
:	2
:	CHF 123.90
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	688
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Along with a review of general developments relating to bivariate distributions, this volume also covers copulas, a subject which has grown immensely in recent years. In addition, it examines conditionally specified distributions and skewed distributions.

	Preface	6
	Contents	8
	Univariate Distributions	36
	Introduction	36
	Notation and Definitions	37
	Notation	37
	Explanations	38
	Characteristic Function	38
	Cumulant Generating Function	39
	Some Measures of Shape Characteristics	40
	Location and Scale	40
	Skewness and Kurtosis	40
	Tail Behavior	41
	Some Multiparameter Systems ofUnivariate Distributions	41
	Reliability Classes	42
	Normal Distribution and Its Transformations	42
	Normal Distribution	42
	Lognormal Distribution	43
	Truncated Normal	43
	Johnson's System	43
	Box--Cox Power Transformations to Normality	44
	g and h Families of Distributions	44
	Efron's Transformation	45
	Distribution of a Ratio	45
	Compound Normal Distributions	45
	Beta Distribution	46
	The First Kind	46
	Uniform Distribution	47
	Symmetric Beta Distribution	47
	Inverted Beta Distribution	47
	Exponential, Gamma, Weibull, and Stacy Distributions	48
	Exponential Distribution	48
	Gamma Distribution	49
	Chi-Squared and Chi Distributions	49
	Weibull Distribution	50
	Stacy Distribution	50
	Comments on Skew Distributions	51
	Compound Exponential Distributions	51
	Aging Distributions	52
	Marshall and Olkin's Family of Distributions	52
	Families of Generalized Weibull Distributions	53
	Logistic, Laplace, and Cauchy Distributions	54
	Logistic Distribution	54
	Laplace Distribution	54
	The Generalized Error Distribution	55
	Cauchy Distribution	55
	Extreme-Value Distributions	55
	Type 1	55
	Type 2	56
	Type 3	56
	Pareto Distribution	56
	Pearson System	57
	Burr System	58
	t- and F-Distributions	58
	t-Distribution	58
	F-Distribution	59
	The Wrapped t Family of Circular Distributions	59
	Noncentral Distributions	60
	Skew Distributions	60
	Skew-Normal Distribution	60
	Skew t-Distributions	61
	Skew-Cauchy Distribution	62
	Jones' Family of Distributions	63
	Some Lesser-Known Distributions	63
	Inverse Gaussian Distribution	63
	Meixner Hypergeometric Distribution	64
	Hyperbolic Distributions	64
	Stable Distributions	64
	References	65
	Bivariate Copulas	68
	Introduction	68
	Basic Properties	69
	Further Properties of Copulas	70
	Survival Copula	71
	Archimedean Copula	72
	Extreme-Value Copulas	73
	Archimax Copulas	74
	Gaussian, t-, and Other Copulas of theElliptical Distributions	75
	Order Statistics Copula	76
	Polynomial Copulas	76
	Approximation of a Copula by a Polynomial Copula	78
	Measures of Dependence Between Two Variables with a Given Copula	79
	Kendall's Tau	79
	Spearman's Rho	80
	Geometry of Correlation Under a Copula	80
	Measure Based on Gini's Coefficient	81
	Tail Dependence Coefficients	81
	A Local Dependence Measure	83
	Tests of Dependence and Inferences	83
	``Concepts of Dependence	83