One-Dimensional Stable Distributions (Translations of Mathematical Monographs - Vol 65)

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