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A Software Tool for Analyzing Stochastic Data
Lipták, Juraj ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
This thesis discusses the possibility of modeling stochastic processes. Elements of the system with the source of randomness in some cases may be represented by probability distribution. The reader will be acquainted with methods of statistical induction for selecting suitable distribution and generating random numbers. Tool developed in this project aims to propose appropriate probability distribution based on empirical data and provide random variable generating with proposed distribution.
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Testing exponentiality
Dvoranová, Romana ; Anděl, Jiří (advisor) ; Hušková, Marie (referee)
This bachelor thesis focuses on detailed review of a selection of tests for exponentiality and their comparison. This text presents classical methods for goodness-of-fit testing for exponentiality, as well as the most recent tests for exponentiality published in the last decades. Based on the characterisation of exponential distribution that is being used, the review includes $\chi^2$ goodness-of-fit tests, tests based on empirical distribution function using Kolmogorov-Smirnov and Cramér-von Misés test statistics, as well as tests based on integral transforms, entropy, mean residual life function, Gini index and others. In particular, this bachelor thesis focuses on tests for exponentiality based on entropy characterisation, e.g. using Shannon, Rényi or cumulative residual entropy. Finally, this thesis includes simulation study comparing power of several more recent tests for exponentiality that have been theoretically described. Powered by TCPDF (www.tcpdf.org)
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Distribution of interpoint distances
Horská, Šárka ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
This thesis investigates basic properties of the interpoint distances be- tween random vectors drawn from multinomial distribution. We also describe a possible application to testing sparse observations, i.e., a setup with small number of observations and large number of categories, where the classical χ2 -test cannot be recommended. As an alternative, utilizing the multinomial interpoint distances, we will present the test statistic proposed by Biswas and Ghosh (2014). 1
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Tests for the Poisson distribution
Trusina, Filip ; Pawlas, Zbyněk (advisor) ; Nagy, Stanislav (referee)
In this work we deal with the question whether a sequence of independent identically distributed random variables comes from the Poisson distribution. For this task we present two different approaches and couple of tests for each appro- ach. The first approach is based on the asymptotic approximation of distribution of test statistics. The second approach uses generation of test samples. Based on simulations done by us, we discuss the power of individual tests and their advantages and disadvantages. 1
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Testing exponentiality
Dvoranová, Romana ; Anděl, Jiří (advisor) ; Hušková, Marie (referee)
This bachelor thesis focuses on detailed review of a selection of tests for exponentiality and their comparison. This text presents classical methods for goodness-of-fit testing for exponentiality, as well as the most recent tests for exponentiality published in the last decades. Based on the characterisation of exponential distribution that is being used, the review includes $\chi^2$ goodness-of-fit tests, tests based on empirical distribution function using Kolmogorov-Smirnov and Cramér-von Misés test statistics, as well as tests based on integral transforms, entropy, mean residual life function, Gini index and others. In particular, this bachelor thesis focuses on tests for exponentiality based on entropy characterisation, e.g. using Shannon, Rényi or cumulative residual entropy. Finally, this thesis includes simulation study comparing power of several more recent tests for exponentiality that have been theoretically described. Powered by TCPDF (www.tcpdf.org)
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A Software Tool for Analyzing Stochastic Data
Lipták, Juraj ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
This thesis discusses the possibility of modeling stochastic processes. Elements of the system with the source of randomness in some cases may be represented by probability distribution. The reader will be acquainted with methods of statistical induction for selecting suitable distribution and generating random numbers. Tool developed in this project aims to propose appropriate probability distribution based on empirical data and provide random variable generating with proposed distribution.
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Goodness-of-fit test for the AFT model based on martingale residuals
Novák, Petr
The Accelerated Failure Time model presents a way how to easily describe survival data with regression on covariates. It is assumed that each observed unit ages internally faster or slower, depending on the covariate values. To use the model properly, we want to check if observed data fit the model assumptions. In the present work we introduce a goodness-of-fit statistics based on modern martingale theory. On simulated data we try to estimate empirical properties of the test for various situations.
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