The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance

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Springer Science & Business Media, May 18, 2001 - Mathematics - 349 pages
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The aim of this monograph is quite modest: It attempts to be a systematic exposition of all that appeared in the literature and was known to us by the end of the 20th century about the Laplace distribution and its numerous generalizations and extensions. We have tried to cover both theoretical developments and applications. There were two main reasons for writing this book. The first was our conviction that the areas and situations where the Laplace distribution naturally occurs is so extensive that tracking the original sources is unfeasible. The second was our observation of the growing demand for statistical distributions having properties tangent to those exhibited by the Laplace laws. These two "necessary" conditions justified our efforts that led to this book. Many details are arranged primarily for reference, such as inclusion of the most commonly used terminology and notation. In several cases, we have proposed unification to overcome the ambiguity of notions so often present in this area. Personal taste may have done some injustice to the subject matter by omitting or emphasizing certain topics due to space limitations. We trust that this feature does not constitute a serious drawback-in our literature search we tried to leave no stone unturned (we collected over 400 references).
 

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Contents

Historical Background
3
Classical Symmetric Laplace Distribution
15
21 Definition and basic properties
16
22 Representations and characterizations
22
23 Functions of Laplace random variables
35
24 Further properties
46
25 Order statistics
53
26 Statistical inference
64
68 Linear transformations
254
69 Infinite divisibility properties
256
610 Stability properties
258
611 Linear regression with Laplace errors
261
612 Exercises
268
Applications
273
Introduction
275
Engineering Sciences
277

27 Exercises
112
Asymmetric Laplace Distributions
133
31 Definition and basic properties
136
32 Representations
144
33 Simulation
149
34 Characterizations and further properties
150
35 Estimation
158
36 Exercises
174
Related Distributions
179
42 Laplace motion
193
43 Linnik distribution
199
44 Other cases
219
45 Exercises
222
Multivariate Distributions
227
Introduction
229
Symmetric Multivariate Laplace Distribution
231
52 General symmetric multivariate case
234
53 Exercises
236
Asymmetric Multivariate Laplace Distribution
239
Definition and basic properties
240
62 General multivariate asymmetric case
243
63 Representations
246
64 Simulation algorithm
248
65 Moments and densities
249
66 Unimodality
251
67 Conditional distributions
253
72 Encoding and decoding of analog signals
280
73 Optimal quantizer in image and speech compression
281
74 Fracture problems
284
75 Wind shear data
285
76 Error distributions in navigation
286
Financial Data
289
82 Interest rate data
290
83 Currency exchange rates
292
84 Share market return models
294
85 Option pricing
296
86 Stochastic variance ValueatRisk models
297
87 A jump diffusion model for asset pricing with Laplace distributed jumpsizes
300
88 Price changes modeled by Laplace Weibull mixtures
302
Inventory Management and Quality Control
303
92 Acceptance sampling for Laplace distributed quality characteristics
304
93 Steam generator inspection
306
95 Duplicate checksampling of the metallic content
308
Astronomy and the Biological and Environmental Sciences
309
102 Pulses in long bright gammaray bursts
310
103 Random fluctuations of response rate
311
104 Modeling low dose responses
312
106 ARMA models with Laplace noise in the environmental time series
313
Bessel Functions
315
References
319
Index
343
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