The Laplace distribution and generalizations拉普拉斯分布和普遍性
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作者： Samuel Kotz，Tomasz Kozubowski，Krzystof Podgorski著
出 版 社：
出版时间： 2001-5-1字数：版次： 1页数： 349印刷时间： 2001/05/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780817641665包装： 精装内容简介
This monograph focuses on the importance of the Laplace distribution and describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. After presenting an historical introduction to the subject, the authors collect and present in a systematic way the univariate Laplace distribution, knowledge of which until now has been scattered in the vast statistical, engineering, and mathematical literature. The multivariate and skewed Laplace distribution are discussed here for the first time in detailed monograph form. Generalizations of Laplace distributions and stochastic processes to which they lead are presented as well. Many results, particularly those on the multivariate and skewed Laplace distribution, appear in print for the first time. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance. Key to the growing interest in the Laplace distribution are its applications, in particular, financial applications. The book covers interesting and recent applications of models based on the Laplace distribution, and will serve as a guide to development in this area of applied research for a broad audience of statisticians, finance experts, economists, engineers, and health scientists. Finally, in opening a new field of research in the theory of statistical distributions, The Laplace Distribution and Generalizations should strongly appeal to those working in theoretical or applied probability theory.
目录
Preface
Abbreviations
Notation
ⅠUnivariate Distributions
1Historical Background
2Classical Symmetric Laplace Distribution
2.1 Definition and basic properties
2.1.1 Density and distribution functions
2.1.2 Characteristic and moment generating functions
2.1.3 Moments and related parameters
2.1.3.1 Cumulants
2.1.3.2 Moments
2.1.3.3 Mean deviation
2.1.3.4 Coefficients of skewness and kurtosis
2.1.3.5 Entropy
2.1.3.6 Quartiles and quantiles
2.2 Representations and characterizations
2.2.1 Mixture of normal distributions
2.2.2 Relation to exponential distribution
2.2.3 Relation to the Pareto distribution
2.2.4 Relation to 2 x 2 unit normal determinants
2.2.5 An orthogonal representation
2.2.6 Stability with respect to geometric summation
2.2.7 Distributional limits of geometric sums
2.2.8 Stability with respect to the ordinary summation
2.2.9 Distributional limits of deterministic sums
2.3 Functions of Laplace random variables
2.3.1 The distribution of the sum of independent Laplace variates
2.3.2 The distribution of the product of two independent Laplace variates
2.3.3 The distribution of the ratio of two independent Laplace variates
2.3.4 The t-statistic for a double exponential (Laolace) distribution
2.4 Further properties
2.4.1 Infinite divisibility
2.4.2 Geometric infinite divisibility
2.4.3 Self-decomposability
2.4.4 Complete monotonicity
2.4.5 Maximum entropy property
2.5 Order statistics
2.5.1 Distribution of a single order statistic
2.5.1.1 The minimum
2.5.1.2 The maximum
2.5.1.3 The median
2.5.2 Joint distributions of order statistics
2.5.2.1 Range, midrange, sample median
2.5.3 Moments of order statistics
2.5.4 Representation of order statistics via sums of exponentials
2.6 Statistical inference
2.6.1 Point estimation
2.6.1.1 Maximum likelihood estimation
2.6.1.2 Maximum likelihood estimation under censoring
2.6.1.3 Maximum likelihood estimation of monotone location parameters
2.6.1.4 The method of moments
2.6.1.5 Linear estimation
2.6.2 Interval estimation
2.6.2.1 Confidence bands for the Laplace distribution function
2.6.2.2 Conditional inference
2.6.3 Tolerance intervals
2.6.4 Testing hypothesis
2.6.4.1 Testing the normal versus the Laplace
2.6.4.2 Goodness-of-fit tests
2.6.4.3 Neyman-Pearson test for location
2.6.4.4 Asymptotic optimality of the Kolmogorov-Smirnov test
2.6.4.5 Comparison of nonparametric tests of location
2.7 Exercises
3Asymmetric Laplace Distributions
3.1 Definition and basic properties
3.1.1 An alternative parametrization and special cases
3.1.2 Standardization
3.1.3 Densities and their properties
3.1.4 Moment and cumulant generating functions
……
4 Related Distributions
ⅡMultivariate Distributions
Intrduction
5 Symmetric Multivariate laplace Distribution
6 Asymmetric Multivariate Laplace Distribution
ⅢApplications
Introdution
7 Engineer Sciences
8 Financial Data
9 Inventory Management and Quality Control
10 Astronomy and the Biologial and Envirnmental Sciences
Appendix:Bessel Functions
References
Index
