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Tennis match modelling using Markov chains
Walica, Roman ; Hübnerová, Zuzana (referee) ; Hrabec, Pavel (advisor)
This thesis deals with the application of Markov chains in the tennis field and their subsequent adjustment based on formulated hypotheses. The first part of thesis describes the principles of the tennis game. In the second part, we deal with concepts from the field of statistics. These concepts are mainly used for creation and subsequent branching of Markov chains. The result of this work is several Markov chains for the game, divided by tennis serve or reception or by the type of surface on which the match is played. The other chains mentioned are chains for tiebreak, set and match. In final part of thesis we introduce obtained prediction of the result and the duration of the tennis match and its modeled parts.
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Testing equivalence and noninferiority
Rychterová, Nela ; Antoch, Jaromír (advisor) ; Omelka, Marek (referee)
This master thesis deals with topics related to the task whether customers are able to recognize a difference between products. First, testing of equivalence and non-inferiority is discussed in detail. It is an important tool when verifying that two products are equivalent or that a new product is not substantially worse than a current product. Afterwards, Thurstone's approach is introduced as a way to evaluate the impact of a stimulus on human senses. Subsequently, using the previous chapters, there is a detailed discussion dealing with three standards wi- dely used in practice in the case when someone needs to apply sensory evaluation to verify whether customers are able to recognize a difference between products. In particular, these are duo-trio, triangle and paired comparison tests. There is a thorough explanation of their statistical base and the tests are compared accor- ding to their power. Furthermore, an approach based on the Thurstone's theory is introduced as an alternative to the standard methods. Moreover, this thesis introduces Saaty's approach to the estimation of a priority vector, which is a useful tool to compare, to order or to choose the best one from n objects. We also introduce another approach to estimation of a priority vector which is based on Saaty's idea. 1
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The specifics of speech from mothers with young children
AŠKOVÁ, Tereza
This diploma thesis follows my bachelor thesis in which the mother slang was described. This diploma thesis is aimed at the performance of the mother speech research, i.e. the use of specific expressions and language resources used by mothers of small children in Internet discussions in relevant forums or web pages. The diploma thesis aims at creating a questionnaire and establishing five hypotheses. The first part of the thesis describes the methodology of this research, in the following part there are presented the data obtained by the questionnaire survey. The hypotheses are verified in the following section, and the hypothesis testing procedure is described here. The appendix includes the questionnaire and a table of critical values that specifies the data that are needed for verifying hypotheses.
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Stability in Autoregressive Time Series Models
Dvořák, Marek ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee) ; Picek, Jan (referee)
The main subject of this thesis is a change point detection in stationary vector autoregressions. Various test statistics are proposed for the retrospective break point detection in the parameters of such models, in particular, the derivation of their asymptotic distribution under the null hypothesis of no change. Testing procedures are based on the maximum like- lihood principle and are derived under normality, nevertheless the asymptotic results are valid for broader class of distributions and involve also the models with certain form of dependence. Simulation studies document the quality of the results.
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Exponenciální třídy a jejich význam pro statistickou inferenci
Moneer Borham Abdel-Maksoud, Sally ; Hlubinka, Daniel (advisor) ; Antoch, Jaromír (referee)
Title: Exponential families in statistical inference Author: Sally Abdel-Maksoud Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D. Supervisor's e-mail address: Daniel.Hlubinka@mff.cuni.cz Abstract: This diploma thesis provides an evaluation of Exponential families of distributions which has a special position in mathematical statistic including appropriate properties for estimation of population parameters, hypothesis testing and other inference problems. Diploma will introduce the basic concepts and facts associated with the distribution of exponential type especially with focusing on the advantages of exponential families in classical parametric statistics, thus in theory of estimation and hypothesis testing. Emphasis will be placed on one-parameter and multi- parameters systems. It also exposes an important concepts about the curvature of a statistical problem including the curvature in exponential families. We will define a quantity that measure how nearly "exponential" the families are. This quantity is said to be the statistical curvature of the family. We will show that the family with a small curvature enjoy the good properties of exponential families Moreover, the properties of the curvature, hypotheses testing and some...
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