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Regression and correlation analysis of time development of the traffic accidents number at transportation of dangerous substances in a selected region.
VÁVRA, Martin
The aim of this thesis was to conduct a statistical survey and the measurement of statistical dependences of time development of the traffic accident rate at transportation of dangerous solid, liquid and gaseous substances, including their total number and also in case of leakage of these substances in a selected region "the Czech Republic". The purpose of the thesis was to verify statistical data, or more precisely, verification of two basic hypotheses H1 and H2, and five sub-hypotheses H11, H12, H13, H14, H15. For these verifications methods of descriptive and mathematical statistics were used, especially regression and correlation analysis in hypothesis H1. To verify hypothesis H2, nonparametric normality test as a technique of mathematical statistics was applied. Verification of hypotheses H1 and their sub-hypotheses H11, H12, H13, H14, H15 enabled to prove linear regression associated with negative correlation within the development of traffic accidents at transportation of dangerous substances in annual units of time (2002 to 2011). Verification of hypothesis H2 enabled to demonstrate normality in distribution of the number of accidents at transportation of dangerous substances within individual months of the monitored period from 2007 to 2011. As benefits of this thesis both the proposal of the sequence of statistical methods for examining the research topic and the application of the mentioned statistical methods to the number of traffic accidents at transportation of dangerous substances can be considered Based on the results of this study, possible follow-up research work may be suggested. A research is proposed which would survey the ways of prevention or other factors leading to negative correlation dependence. Another possibility of follow-up research work could be, for example, statistical surveys and the measurement of statistical dependences in regions of the CR or investigation of the theoretical distribution of the number of traffic accidents at transportation of dangerous substances within a different time unit.
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Teaching System for Study Support of Advanced Statistics
Homolová, Jitka ; Nagy, Ivan
The paper describes the tproposed teaching system for advanced statstics for PhD. students of technical universities. There are several conditions on them: to use technical instrumentations, to present mathematical texts of high quality, to be easily available whencesoever and to use only free open software. The whole teaching system needs to be as simple as possible. It has to be well arranged and described with corresponding manual enclosed.
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Teaching system of applied statistics
Homolová, Jitka ; Nagy, Ivan
A teaching system for study support of applied statistics presented by matematical text in a close connection with software realization of the results is presented. For cerating texts, the "pdf-version" of mathematical text editor is used. For software application, the interactive programming langeuge GNU Octave is exploited.Both the texts and programs are free, the subroutines used are open.
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Statistical survival analysis and random point processes
Volf, Petr
The paper is devoted to statistical survival analysis, discusses different probabilistic models including the Cox model of regression for the intensity of time to failure. Then, the concept of counting processes in recalled and their models (including Cox regression) is used for characterization of random point processes of repeated events (e.g. failures and repairs).
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On regression models of survival analysis and application to grouped unemployment data
Volf, Petr
The contribution deals with the Cox's regression model and with its application to the analysis of group ed data, when both the numbers of followed objects and the numbers of observed events are summarized in discrete time periods and covariate classes. The formulation of the model and the procedure of estimation of its parameters are presented. A numerical example shows the analysis of grouped unemployment data.
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Statistical models and analysis of growing damage processes
Volf, Petr
We deal with the reliability analysis of technical devices and consider the processes of gradually growing damage caused by random shocks or other events. The cumulation of damage modeled via the random cumulative processes, generalization of Poisson process with random increments. The methods of statistical analysis and an example are presented.
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