Browsing Mathematics by Title

Miličić, Miloš (Belgrade , 1982)[more][less]

Malinović, Todor (Novi Sad , 1986)[more][less]

Obradović, Marko (Beograd , 2015)[more][less]
Abstract: First characterizations of probability distributions date to the thirties of last century. This area, which lies on the borderline of probability theory and mathematical statistics, attracts large number of researchers, and in recent times the number of papers on the subject is increasing. Goodnessof t tests are among the most important nonparametric tests. Many of them are based on empirical distribution function. The application of characterization theorems for construction of goodnessof t tests dates to the middle of last century, and recently has become one of the main directions in this eld. The advantage of such tests is that they are often free of distribution parametres and hence enable testing of composite hypotheses. The goals of this dissertation are the formulation of new characterizations of exponential and Pareto distribution, as well as the application of the theory of Ustatistics, large deviations and Bahadur e ciency to construction and examination of asymptotics of goodnessof t tests for aforementioned distributions. The dissertation consists of six chapters. In the rst chapter a review of di erent types of characterizations is presented, pointing out their abundance and variety. The special emphasis is given to the characterizations based on equidistribution of functions of the sample. Besides, two new characterizations of Pareto distribution are presented. The second chapter is devoted to some new characterizations of the exponential distributions presented in papers [65] and [53]. Six characterizations based on order statistics are presented. A special case of one of them (theorem 2.4.3) represents the solution of open problem stated by Arnold and Villasenor [9]. In the third chapter there are basic concepts on Ustatistics, the class of statistics important in the theory of unbiased estimation. Some of their asymptotic properties are given. Uempirical distribution functions, a generalization of standard empirical distribution functions, are also de ned. The fourth chapter is dedicated to the asymptotic e ciency of statistical tests, primarily to Bahadur asymptotic e ciency, i.e. asymptotic e ciency of the test when the level of signi cance approaches zero. Some theoretical results from the monograph by Nikitin [57], and papers [61], [59], etc. are shown. In the fth chapter new results in the eld of goodnessof t tests for Pareto distribution are presented. Based on three characterizations of Pareto distribution given in section 1.1.2. six goodnessof t tests, three of integral, and three of Kolmogorov type, are proposed. In each case the composite null hypothesis is tested since the test statistics are free of the parameter of Pareto distribution. For each test the asymptotic distribution under null hypothesis, as well as asymptotic behaviour of the tail (large deviations) under close alternatives is derived. For some standard alternatives, the local Bahadur asymptotic e ciency is calculated and the domains of local asymptotic optimality are obtained. The results from this chapter are published in [66] and [64]. The sixth chapter brings new goodnessof t tests for exponential distribution. Based on the solved hypothesis of Arnold and Villasenor two classes of tests, integral and Kolmogorov type, are proposed, depending on the number of summands in the characterization. The study of asymptotic properties, analogous to the ones in the fth chapter is done in case of two and three summands, for which the tests have practical importance. The results of this chapter are presented in [39]. URI: http://hdl.handle.net/123456789/4288 Files in this item: 1
phdObradovicMarko.pdf ( 789.3Kb ) 
Aranđelović, Dragoljub (Belgrade)[more][less]

Alagić, Mara (Belgrade , 1985)[more][less]

Jokanović, Dušan (Podgorica)[more][less]

Stojadinović, Tanja (Univerzitet u Beogradu , 2014)[more][less]
Abstract: Multiplication and comultiplication, which de ne the structure of a Hopf algebra, can naturally be introduced over many classes of combinatorial objects. Among such Hopf algebras are wellknown examples of Hopf algebras of posets, permutations, trees, graphs. Many classical combinatorial invariants, such as M obius function of poset, the chromatic polynomial of graphs, the generalized DehnSommerville relations and other, are derived from the corresponding Hopf algebra. Theory of combinatorial Hopf algebras is developed by Aguiar, Bergerone and Sottille in the paper from 2003. The terminal objects in the category of combinatorial Hopf al gebras are algebras of quasisymmetric and symmetric functions. These functions appear as generating functions in combinatorics. The subject of study in this thesis is the combinatorial Hopf algebra of hyper graphs and its subalgebras of building sets and clutters. These algebras appear in di erent combinatorial problems, such as colorings of hypergraphs, partitions of sim plicial complexes and combinatorics of simple polytopes. The structural connections among these algebras and among their odd subalgebras are derived. By applying the character theory, a method for obtaining interesting numerical identities is pre sented. The generalized DehnSommerville relations for ag fvectors of eulerian posets are proven by Bayer and Billera. These relations are de ned in an arbitrary com binatorial Hopf algebra and they determine its odd subalgebra. In this thesis, the generalized DehnSommerville relations for the combinatorial Hopf algebra of hy pergraphs are solved. By analogy with Rota's Hopf algebra of posets, the eulerian subalgebra of the Hopf algebra of hypergraphs is de ned. The combinatorial char acterization of eulerian hypergraphs, which depends on the nerve of the underlying clutter, is obtained. In this way we obtain a class of solutions of the generalized DehnSommerviller relations for hypergraphs. These results are applied on the Hopf algebra of simplicial complexes. URI: http://hdl.handle.net/123456789/3745 Files in this item: 1
phdTanjaStojadinovic.pdf ( 13.95Mb ) 
Stojadinović, Tanja (Beograd , 2013)[more][less]
Abstract: Multiplication and comultiplication, which de ne the structure of a Hopf algebra, can naturally be introduced over many classes of combinatorial objects. Among such Hopf algebras are wellknown examples of Hopf algebras of posets, permutations, trees, graphs. Many classical combinatorial invariants, such as M obius function of poset, the chromatic polynomial of graphs, the generalized DehnSommerville relations and other, are derived from the corresponding Hopf algebra. Theory of combinatorial Hopf algebras is developed by Aguiar, Bergerone and Sottille in the paper from 2003. The terminal objects in the category of combinatorial Hopf algebras are algebras of quasisymmetric and symmetric functions. These functions appear as generating functions in combinatorics. The subject of study in this thesis is the combinatorial Hopf algebra of hypergraphs and its subalgebras of building sets and clutters. These algebras appear in di erent combinatorial problems, such as colorings of hypergraphs, partitions of simplicial complexes and combinatorics of simple polytopes. The structural connections among these algebras and among their odd subalgebras are derived. By applying the character theory, a method for obtaining interesting numerical identities is presented. The generalized DehnSommerville relations for ag fvectors of eulerian posets are proven by Bayer and Billera. These relations are de ned in an arbitrary combinatorial Hopf algebra and they determine its odd subalgebra. In this thesis, the generalized DehnSommerville relations for the combinatorial Hopf algebra of hypergraphs are solved. By analogy with Rota's Hopf algebra of posets, the eulerian subalgebra of the Hopf algebra of hypergraphs is de ned. The combinatorial characterization of eulerian hypergraphs, which depends on the nerve of the underlying clutter, is obtained. In this way we obtain a class of solutions of the generalized DehnSommerviller relations for hypergraphs. These results are applied on the Hopf algebra of simplicial complexes. URI: http://hdl.handle.net/123456789/4306 Files in this item: 1
phdTanjaStojadinovic.pdf ( 13.95Mb ) 
Shafah, Osama (Beograd , 2013)[more][less]

Protić, Petar (Novi Sad , 1986)[more][less]

Vulanović, Relja (Novi Sad , 1986)[more][less]

Šarac, Marica (Belgrade)[more][less]

Romano, Daniel (Belgrade , 1985)[more][less]

Veljković, Kristina (Beograd , 2016)[more][less]
Abstract: Design of control chart for monitoring central tendency of nongaussian random variables with symmetric or positively skewed distributions is considered. In the case of nongaussian symmetric distributions, modified X bar control chart is proposed in this dissertation. For chosen Student, Laplace, logistic and uniform distributions, theoretical distribution of the standardized sample mean is calculated and approximated with Pearson type II or Pearson type VII distributions. Width of control limits and power of X bar control chart are established, for a given probability of type I error. The results imply that the corresponding Pearson distribution represents very good approximation of the distribution of the standardized sample mean. For implementation of X bar control chart in practice, measures of sample kurtosis are compared and the usage of proposed chart is illustrated on given data. In the case of positively skewed distributions, one sided median control chart for monitoring central tendency of quality characteristics is proposed in this dissertation. For chosen exponential, gamma and Weibull distributions, theoretical distribution of sample median is calculated and approximated with Pearson type I or Pearson type VI distributions. Calculated values of upper control limits and power of median control chart for theoretical distribution of sample median and corresponding Pearson distribution are very close. For implementation of median control chart in practice, measures of sample skewness and sample kurtosis are compared and then proposed median chart is constructed for given data. Besides the statistical design of control charts for monitoring central tendency of nongaussian random variables, their optimal economic statistical design is also considered. Use of genetic algorithms for constrained minimization of expected loss function is proposed in this dissertation. Same symmetric distributions as in the case of statistical design of the X bar control chart and positively skewed distributions as in the case of statistical design of median control chart are chosen. For all chosen distributions of quality characteristic, a corresponding Pearson distribution gives results very close to results based on the theoretical distribution of the standardized sample mean (sample median). URI: http://hdl.handle.net/123456789/4449 Files in this item: 1
Kristinateza.pdf ( 2.651Mb ) 
Dražić, Milan (Beograd , 1995)[more][less]

Dražić, Milan (Beograd , 1995)[more][less]

Takači, Arpad (Novi Sad , 1981)[more][less]

Nikić, Mioljub (Belgrade)[more][less]

Blažić, Novica (Belgrade)[more][less]

Krstić, Sava (Belgrade)[more][less]