000			04008cam a22003497i 4500
999			_c880 _d880
001			17518772
003			OSt
005			20200804093859.0
008			121105s2013 nyua b 001 0 eng d
010			_a 2012953265
016	7		_a016210726 _2Uk
020			_a9781461448686 (hbk. : alk. paper)
035			_a(OCoLC)ocn798062468
040			_aBTCTA _beng _cKCST
042			_alccopycat
050	0	0	_aQA273.45 _b.M48 2013
082	0	4	_a519.2 _223
245	0	4	_aThe methods of distances in the theory of probability and statistics / _cSvetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi.
260			_aLondon : _bSpringer, _c2013.
300			_axvi, 619 pages : _billustrations ; _c25 cm
504			_aIncludes bibliographical references and index.
505	0	0	_tGeneral topics in the theory of probability metrics -- _tProbability Distances and Probability Metrics: Definitions -- _tPrimary, Simple, and Compound Probability Distances and Minimal and Maximal Distances and Norms -- _tA Structural Classification of Probability Distances -- _tRelations between compound, simple and primary distances -- _tMonge-Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms -- _tQuantitative Relationships Between Minimal Distances and Minimal Norms -- _tK -Minimal Metrics -- _tRelations Between Minimal and Maximal Distances -- _tMoment Problems Related to the Theory of Probability Metrics: Relations Between Compound and Primary Distances -- _tApplications of minimal probability distances -- _tMoment Distances -- _tUniformity in Weak and Vague Convergence -- _tGlivenko-Cantelli Theorem and Bernstein-Kantorovich Invariance Principle -- _tStability of Queueing Systems -- _tOptimal Quality Usage / _rSvetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi -- _tIdeal metrics -- _tIdeal Metrics with Respect to Summation Scheme for i.i.d. Random Variables -- _tIdeal Metrics and Rate of Convergence in the CLT for Random Motions -- _tApplications of Ideal Metrics for Sums of i.i.d. Random Variables to the Problems of Stability and Approximation in Risk Theory -- _tHow Close Are the Individual and Collective Models in Risk Theory? -- _tIdeal Metric with Respect to Maxima Scheme of i.i.d. Random Elements -- _tIdeal Metrics and Stability of Characterizations of Probability Distributions -- _tEuclidean-like distances and their applications -- _tPositive and Negative Definite Kernels and Their Properties -- _tNegative Definite Kernels and Metrics: Recovering Measures from Potentials -- _tStatistical Estimates Obtained by the Minimal Distances Method -- _tSome Statistical Tests Based on N -Distances -- _tDistances Defined by Zonoids -- _tN -Distance Tests of Uniformity on the Hypersphere.
520			_aThis 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.-- _cSource other than Library of Congress.
650		0	_aProbabilities. _91388
650		0	_aMathematical statistics. _91389
650		0	_aCombinatorial probabilities. _94574
700	1		_aRachev, S. T. _q(Svetlozar Todorov) _94576
700	1		_aKlebanov, L. B. _q(Lev Borisovich), _d1946- _94577
700	1		_aStoyanov, Stoyan V. _94578
700	1		_aFabozzi, Frank J. _94579
942			_2ddc _cBO