## The Laplace Distribution and Generalizations: A Revisit With Applications to Communications, Exonomics, Engineering, and FinanceThis 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. |

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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 |

319 | |

343 | |

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The Laplace Distribution and Generalizations: A Revisit With **...**

The Laplace Distribution and Generalizations: A Revisit With Applications to Communications, Economics, Engineering, and Finance from Journal of the ...

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Approximating the distributions of estimators of financial risk **...**

The Laplace Distribution and Generalizations: a Revisit with Applications to Communications, Economics, Engineering, and Finance. Birkhäuser, Boston. ...

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KRZYSZTOF PODGORSKI Professor

KRZYSZTOF PODGORSKI. Professor. Centre for Mathematical Sciences. Mathematical Statistics. Lund University. Box 118. 221 00 Lund ...

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2003 Royal Statistical Society. 0039–0526/03/52689. The Statistician (2003). 52. ,. Part 4. ,. pp. 689–705. Book reviews. Books for review ...

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