توزیع‌های پایدار یک‌بعدی (ترجمه‌های مونوگراف‌های ریاضی - جلد 65)

This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws. Title......Page 0001_0001.djvu Contents......Page 0003_0001.djvu Foreword......Page 0005_0001.djvu Introduction......Page 0009_0001.djvu 1.0. Introduction......Page 0033_0001.djvu 1.1. A model of point sources of influence......Page 0039_0001.djvu 1.2. Stable laws in problems in radio engineering and electronics......Page 0056_0001.djvu 1.3. Stable laws in economics and biology......Page 0062_0001.djvu 2.1. Elementary properties of stable laws......Page 0067_0001.djvu 2.2. Representation of stable laws by integrals......Page 0073_0001.djvu 2.3. The duality law in the class of strictly stable distributions......Page 0089_0001.djvu 2.4. The analytic structure of stable distributions and their representation by convergent series......Page 0095_0001.djvu 2.5. Asymptotic expansions of stable distributions......Page 0100_0001.djvu 2.6. Integral transformations of stable distributions......Page 0115_0001.djvu 2.7. Unimodality of stable distributions. The form of the densities......Page 0129_0001.djvu 2.8. Stable distributions as solutions of integral, integrodifferential, and differential equations......Page 0155_0001.djvu 2.9. Stable laws as functions of parameters......Page 0167_0001.djvu 2.10. Densities of stable distributions as a class of special functions......Page 0175_0001.djvu 2.11. Trans-stable functions and trans-stable distributions......Page 0180_0001.djvu 3.0. Introduction......Page 0189_0001.djvu 3.1. The concept of a cutoff of a random variable......Page 0192_0001.djvu 3.2. The random variables Y(...) and Z(...). Equivalence theorems......Page 0195_0001.djvu 3.3. The random variables Y(...) and Z(...). Multiplication and division theorems......Page 0202_0001.djvu 3.4. Properties of extremal strictly stable distributions......Page 0210_0001.djvu 3.5. M-infinite divisibility of the distribu tions of the variables Y(...) and Z(...)......Page 0216_0001.djvu 3.6. The logarithmic moments of Y(...) and Z(...)......Page 0221_0001.djvu 4.0. Introduction......Page 0225_0001.djvu 4.1. Auxiliary facts......Page 0227_0001.djvu 4.2. Estimators of parameters of distributions in the class W......Page 0232_0001.djvu 4.3. Estimators of parameters of distributions in the family S: the parameters alpha, beta, and lambda......Page 0237_0001.djvu 4.4. Estimators of the parameter gamma......Page 0247_0001.djvu 4.5. Discussion of the estimators......Page 0251_0001.djvu 4.6. Simulation of sequences of stable random variables......Page 0256_0001.djvu Comments......Page 0259_0001.djvu Bibliography......Page 0271_0001.djvu List of Notation......Page 0289_0001.djvu Subject Index......Page 0291_0001.djvu Focuses on the analytic properties of stable laws. This book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. V.m. Zolotarev. Translation Of: Odnomernye Ustoĭchivye Raspredelenii︠a︡. Includes Index. Bibliography: P. 263-280.