The Methods of Distances in the Theory of Probability and Statistics

1. Main Directions in the Theory of Probability Metrics
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

2. Probability Distances and Probability Metrics: Definitions
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

3. Primary, Simple, and Compound Probability Distances and Minimal and Maximal Distances and Norms
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

4. A Structural Classification of Probability Distances
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

5. Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

6. Quantitative Relationships Between Minimal Distances and Minimal Norms
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

7.
K -Minimal Metrics
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

8. Relations Between Minimal and Maximal Distances
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

9. Moment Problems Related to the Theory of Probability Metrics: Relations Between Compound and Primary Distances
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

10. Moment Distances
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

11. Uniformity in Weak and Vague Convergence
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

12. Glivenko–Cantelli Theorem and Bernstein–Kantorovich Invariance Principle
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

13. Stability of Queueing Systems
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

14. Optimal Quality Usage
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

15. Ideal Metrics with Respect to Summation Scheme for i.i.d. Random Variables
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

16. Ideal Metrics and Rate of Convergence in the CLT for Random Motions
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

17. Applications of Ideal Metrics for Sums of i.i.d. Random Variables to the Problems of Stability and Approximation in Risk Theory
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

18. How Close Are the Individual and Collective Models in Risk Theory?
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

19. Ideal Metric with Respect to Maxima Scheme of i.i.d. Random Elements
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

20. Ideal Metrics and Stability of Characterizations of Probability Distributions
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

21. Positive and Negative Definite Kernels and Their Properties
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

22. Negative Definite Kernels and Metrics: Recovering Measures from Potentials
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

23. Statistical Estimates Obtained by the Minimal Distances Method
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

24. Some Statistical Tests Based on N
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

25. Distances Defined by Zonoids
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

26.
N-Distance Tests of Uniformity on the Hypersphere
Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

Avainsanat: Mathematics, Probability Theory and Stochastic Processes, Statistical Theory and Methods, Approximations and Expansions