The Methods of Distances in the Theory of Probability and Statistics

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Rachev, Svetlozar T. (Autor), Klebanov, Lev (Autor), Stoyanov, Stoyan V. (Autor), Fabozzi, Frank (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Temas:
Probabilities.
Statistics .
Approximation theory.
Probability Theory.
Statistical Theory and Methods.
Approximations and Expansions.
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-1-4614-4869-3
003 DE-He213
005 20220126123005.0
007 cr nn 008mamaa
008 130107s2013 xxu| s |||| 0|eng d
020 |a 9781461448693  |9 978-1-4614-4869-3 
024 7 |a 10.1007/978-1-4614-4869-3  |2 doi 
050 4 |a QA273.A1-274.9 
072 7 |a PBT  |2 bicssc 
072 7 |a PBWL  |2 bicssc 
072 7 |a MAT029000  |2 bisacsh 
072 7 |a PBT  |2 thema 
072 7 |a PBWL  |2 thema 
082 0 4 |a 519.2  |2 23 
100 1 |a Rachev, Svetlozar T.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Methods of Distances in the Theory of Probability and Statistics  |h [electronic resource] /  |c by Svetlozar T. Rachev, Lev Klebanov, Stoyan V. Stoyanov, Frank Fabozzi. 
250 |a 1st ed. 2013. 
264 1 |a New York, NY :  |b Springer New York :  |b Imprint: Springer,  |c 2013. 
300 |a XVI, 619 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
505 0 |a Main directions in the theory of probability metrics -- Probability distances and probability metrics: Definitions -- Primary, simple and compound probability distances, and minimal and maximal distances and norms -- A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms -- Quantitative relationships between minimal distances and minimal norms -- K-Minimal metrics -- Relations between minimal and maximal distances -- Moment problems related to the theory of probability metrics: Relations between compound and primary distances -- Moment distances -- Uniformity in weak and vague convergence -- Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle -- Stability of queueing systems.-Optimal quality usage -- Ideal metrics with respect to summation scheme for i.i.d. random variables -- Ideal metrics and rate of convergence in the CLT for random motions -- Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory -- How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements -- Ideal metrics and stability of characterizations of probability distributions -- Positive and negative de nite kernels and their properties -- Negative definite kernels and metrics: Recovering measures from potential -- Statistical estimates obtained by the minimal distances method -- Some statistical tests based on N-distances -- Distances defined by zonoids -- N-distance tests of uniformity on the hypersphere.-. 
520 |a This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to  the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.       Svetlozar T.  Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook  and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute-Asia (Singapore).  Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)  . 
650 0 |a Probabilities. 
650 0 |a Statistics . 
650 0 |a Approximation theory. 
650 1 4 |a Probability Theory. 
650 2 4 |a Statistical Theory and Methods. 
650 2 4 |a Approximations and Expansions. 
700 1 |a Klebanov, Lev.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Stoyanov, Stoyan V.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Fabozzi, Frank.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9781461448686 
776 0 8 |i Printed edition:  |z 9781461448709 
776 0 8 |i Printed edition:  |z 9781489995698 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-1-4614-4869-3  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

Ejemplares similares