Browsing by Subject "Probabilities"
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Item A Burr type X chain-of-links model(Texas Tech University, 2001-05) D'Ambrosio, Donna M.In this thesis, the study of the Burr type X (often abbreviated BurrX) family of distributions applied to the chain-of-links model is considered. The Burr type X distribution was introduced by I. W. Burr in 1942. At that time, Burr also introduced eleven other families of distributions to study failure type data. Of the twelve distributions he introduced, only two have garnered substantial attention. The Burr type X is one of those which has received attention. This attention is due to its flexibility and power in fitting many types of observed data. In this thesis, the chain-of-links Burr type X model is derived based on simple mathematical arguments. Once the form is found, various properties of the model are studied. Of particular interest is estimation of, and inference for, the parameters of the model. Estimation is accomplished using maximum likelihood estimation. A large-scale simulation is conducted to study the large sample behavior of the maximum likelihood estimates. The empirical distributions of the estimators are compared to the well-known normal distribution to determine if inference procedures based on the normal distribution are appropriate. If normal-based inference procedures are appropriate, the simulations will allow one to determine for what sample sizes they are applicable. Finally, the simulations will also allow one to determine what factors effect the degree to which the distribution of the maximum likelihood estimates deviate from the normal distribution. Bader and Priest (1982), of the University of Surrey in England, conducted several experiments on carbon fibrous composites. They studied the strengths of individual carbon fibers, and 1000 fiber collections held together by an epoxy resin known as a tow. The Weibull distribution is most often applied to this data set with mixed results. The Weibull model provides a good fit for the individual carbon fibers but provides a less-than-satisfactory fit for the tow data. It has been shown by Surles and Padgett (1998) that the Burr type X model provides good fits for both sets of data. In this thesis, the chain-of-links Burr type X model is applied to the Bader and Priest fiber data. Modified versions of the chain-of-links Burr type X model are also under study. These are known as the linear and power-law models. These models, if seen to be appropriate, allow for the study of a phenomenon known as the end-effect, or clamp effect. The act of testing a fiber generally weakens the ends of the fiber, here it is held in place on the testing device.Item A stochastic wear and failure process(Texas Tech University, 1965-05) Benno, Stephen AllanNot availableItem Approximation of Pearson type IV probability integral(Texas Tech University, 1971-05) Woodward, Wayne AnthonyNot availableItem Continuous Probability Functions Used to Approximate Discrete Distributions(Texas Tech University, 1941-08) Masters, HardyNot Available.Item Coping with dynamic membership, selfishness, and incomplete information: applications of probabilistic analysis and game theory(2008-05) Dimitrov, Nedialko B.; Plaxton, C. GregThe emergence of large scale distributed computing networks has given increased prominence to a number of algorithmic concerns, including the need to handle dynamic membership, selfishness, and incomplete information. In this document, we outline our explorations into these algorithmic issues. We first present our results on the analysis of a graph-based coupon collecvi tor process related to load balancing for networks with dynamic membership. In addition to extending the study of the coupon collector process, our results imply load balancing properties of certain distributed hash tables. Second, we detail our results on worst case payoffs when playing buyersupplier games, against many selfish, collaborating opponents. We study optimization over the set of core vectors. We show both positive and negative results on optimizing over the cores of such games. Furthermore, we introduce and study the concept of focus point price, which answers the question: If we are constrained to play in equilibrium, how much can we lose by playing the wrong equilibrium? Finally, we present our analysis of a revenue management problem with incomplete information, the online weighted transversal matroid matching problem. In specific, we present an algorithm that delivers expected revenue within a constant of optimal in the online setting. Our results use a novel algorithm to generalize several results known for special cases of transversal matroids.Item Heuristic influence on decision processes(Texas Tech University, 1982-12) Klein, Gary LNot availableItem Plog: Its algorithms and applications(2012-05) Zhu, Weijun; Gelfond, Michael; Zhang, Yuanlin; Nelson, RushtonThis dissertation is a contribution towards combining logical and probabilistic reasoning. The work is based on the language P-log which combines a recently developed non-monotonic logic language, Answer Set Prolog, with the philosophy of causal Bayesian networks. The goal of this dissertation was to design and implement an inference engine for P-log and to develop a methodology of its use. As the result of this research work, we had built two P-log inference engines. Through the experiments on various examples, we have shown the advantages of using plog2.0, a system based on partial grounding algorithm and a concept of partial possible worlds. We introduced a new action description language NB which allows specifying non-deterministic actions as well as probabilities associated with these actions. We developed an encoding which maps systems written in NB to P-log programs. We presented systematic methods of representing probabilistic diagnosis and planning problems and algorithms of finding the solutions with P-log systems. Finally, we investigated the performance on these two applications and compared with other similar systems.Item Polynomials that arise in a Polya urn gambling game(Texas Tech University, 2005-05) Hanlon, Bret M.A gambling game based on the Polya urn process is discussed. Working with the expected value of the game produces an interesting sum. The main result of the paper is this sum is a polynomial with degree equal to the initial number of balls in the urn.Item Probabilistic modeling of microelectromechanical systems (MEMS)(Texas Tech University, 2002-12) Khandaker, Morshed P. H.Micro-Electro-Mechanical Systems (MEMS) are a fast-developing technology that have a potential to permeate most engineering and medical applications. For this technology to continue expanding, issues regarding the cost of manufacturing and reliability of the devices have to be addressed. To improve the reliability, probabilistic design methodologies are potent in both the modeling and testing of high-performance MEMS. The benefit of probabilistic design approaches is a more rational basis for making design decisions that balance component or system efficiency with reliability or safety. Probabilistic methods are used to assess uncertainties involved in the manufacturing of MEMS devices. Probabilistic methods guide the design of these devices to achieve reliable design in a most efficient way. The objectives of the research work were to formulate and analyze probabilistic failure criteria on a simplified capacitive accelerometer mode. In this respect, comprehensive probabilistic and deterministic analysis was carried out for the selected model. The scope of work is threefold. First, two probabilistic failure criteria will be investigated on the capacitive structure, namely probabilistic clearance failure criterion and probabilistic fracture toughness failure criterion. Second, four kinds of probabilistic analyses for characterization of MEMS will be used: probability of failure, sensitivity analysis, safety index, and probability-based design. Third, three kinds of finite element analyses, namely static, modal and spectral analysis, will be used to see the deterministic response and will be compared with probabilistic resultItem Smooth Empirical Bayes Estimation of Observation Error Variances in Linear Systems(Texas Tech University, 1971-12) Lian, Mingwei GeorgeNot Available.Item Techniques for the evaluation of the multivariate normal probability integral(Texas Tech University, 1967-06) Ludeman, Michael MartinNot availableItem The order of a perfect k-shuffle(Texas Tech University, 1990-12) Packard, Erik SargentNot availableItem The order of a perfect k-shuffle on a moded-out deck(Texas Tech University, 1995-05) Packard, Erik SargentWhen a deck of n cards is shuffled so that the shuffle is some fixed permutation on n objects, i.e., an element of 5, it is natural to ask how many times this shuffle must be performed before the deck will return to its original configuration. The number of shuffles needed for this to happen is called the order of the shuffle. A perfect 2-shuffle involves dividing an even deck in two halves and then interlacing the cards so they alternate, i.e., how a two- armed person would perfectly shuffle the deck. A precise definition of how this concept would be extended to a A:-armed person is given. For a deck of size ks, it is known that the order of the simplest perfect A:-shuffle is the order of k modulo ks — 1, i.e., the minimum positive integer d such that A:'^ = 1 (mod ks — 1). This dissertation deals with decks in which the cards are not all distinct. The definition of the order of a perfect A;-shuffle is extended to "moded-out" decks, i.e., decks in which the cards repeat in blocks of equal length. This dissertation gives a theorem which gives the order of a perfect A;-shuffle on a "moded-out" deck of size ks. Also given are consequences of the theorem that are related to what is known about the order of a perfect A;-shuffle on a regular deck.