|
|
INAR time series models
Camfrlová, Monika ; Dvořák, Jiří (advisor) ; Hudecová, Šárka (referee)
This work focuses on INAR(1) time series models. The structure of the models is described and the expected value, the variance and the autocovariance function are derived. The next discussed issue is the characterisation of weak stationarity of the INAR(1) models. Three methods of estimation of parame- ters, under the assumption that the random variables describing number of the elements which entered the system in the interval (t−1, t] have Poisson distribu- tion, are described. These methods are compared based on estimations of relative mean square error and of relative bias which were computed from simulations of the process in Mathematica. 1
|
|
|
Entropy and discrete distributions
Kuc, Petr ; Jurečková, Jana (advisor) ; Hlubinka, Daniel (referee)
Shannon entropy of a probability distribution gives a weighted mean of a measure of information that we are given when we observe a ran- dom variable with the distribution. In this thesis we introduce more extensive concept of the term of information entropy and we introduce Shannon entropy as an important special case. Then we compute Shannon entropy for some specific probability distributions, show which distributions have maximal en- tropy under given constraints and we introduce the principle of maximum entropy as a useful estimate of probability models. Another topic of this thesis is an introduction of the principle of minimum divergence by which we can arbitrarily accurately estimate an unknown probability distribution of the given random variable if we have a sufficiently long random sample. Finally we prove that the binomial distribution converges to the Poisson distribution in the Shannon divergence. 1
|
|
|
Postupy pro detekci změny v některých speciálních regresních modelech
Exnarová, Petra ; Hušková, Marie (advisor) ; Antoch, Jaromír (referee)
Title: Detection of change in some special regression models Author: Bc. Petra Exnarová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Marie Hušková, DrSc. Abstract: Presented thesis deals with testing of change in three special cases of change-point analysis. First of them is case of continuous change in linear regression (so-called broken-line model), the other two are related to change in parameters of discrete value distributions - simple case of Bernoulli distributed variables is studied first and then the approach is generalized for case of Multi- nomial distribution. Both situations of known and unknown change point are described for all three cases. Beside approximation by using limit theorems, the bootstrap method and permutation test are described for all studied cases as well. The comparison of critical values gained by different approaches for the particular tests and small power analysis is done using simulations. Keywords: change-point analysis, broken-line model, discrete distribution, boot- strap, permutation test 1
|
|
|
Statistical processing of experimental data
NAVRÁTIL, Pavel
This thesis contains theory of probability and statistical sets. Solved and unsolved problems of probability, random variable and distributions random variable, random vector, statistical sets, regression and correlation analysis. Unsolved problems contains solutions.
|
guest ::
