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This diploma thesis focuses on the statistical examination of properties of plant protection products at Agro-Artikel, s.r.o. Using the empirical distribution function, it focuses on the sales price and the shelf life of the products, tests the hypotheses about the properties of the products and the dependencies between them. The thesis also explores the results of the questionnaire survey and offers recommendations for the introduction of new products.

The actual traffic flow theory assumes interactions only between neighbouring vehicles within the traffic. This assumption is reasonable, but it is based on the possibilities of science and technology available decades ago, which are currently overcome. Obviously, in general, there is an interaction between vehicles at greater distances (or between multiple vehicles), but at the time, no procedure has been put forward to quantify the distance of this interaction. This work introdukce a method, which use mathematical statistics and precise measurement of time distances of individual vehicles, which allows to determine these interacting distances (between several vehicles) and its validation for narrow densities of traffic flow. It has been revealed that at high traffic flow densities there is an interaction between at least three consecutive vehicles and four and five vehicles at lower densities. Results could be applied in the development of new traffic flow models and its verification.

The Birnbaum-Saunders (BS) distribution is a positively skewed distribution and is a popular model for analyzing lifetime data. In this thesis, we first develop an improved method of estimation for the BS distribution and the corresponding inference. Compared to the maximum likelihood estimators (MLEs) and the modified moment estimators (MMEs), the proposed method results in estimators with smaller bias, but having the same mean squared errors (MSEs) as these two estimators. Next, the existence and uniqueness of the MLEs of the parameters of BS distribution are discussed based on Type-I, Type-II and hybrid censored samples. In the case of five-parameter bivariate Birnbaum-Saunders (BVBS) distribution, we use the distributional relationship between the bivariate normal and BVBS distributions to propose a simple and efficient method of estimation based on Type-II censored samples. Regression analysis is commonly used in the analysis of life-test data when some covariates are involved. For this reason, we consider the regression problem based on BS and BVBS distributions and develop the associated inferential methods. One may generalize the BS distribution by using Laplace kernel in place of the normal kernel, referred to as the Laplace BS (LBS) distribution, and it is one of the generalized Birnbaum-Saunders (GBS) distributions. Since the LBS distribution has a close relationship with the Laplace distribution, it becomes necessary to first carry out a detailed study of inference for the Laplace distribution before studying the LBS distribution. Several inferential results have been developed in the literature for the Laplace distribution based on complete samples. However, research on Type-II censored samples is somewhat scarce and in fact there is no work on Type-I censoring. For this reason, we first start with MLEs of the location and scale parameters of Laplace distribution based on Type-II and Type-I censored samples. In the case of Type-II censoring, we derive the exact joint and marginal moment generating functions (MGF) of the MLEs. Then, using these expressions, we derive the exact conditional marginal and joint density functions of the MLEs and utilize them to develop exact confidence intervals (CIs) for some life parameters of interest. In the case of Type-I censoring, we first derive explicit expressions for the MLEs of the parameters, and then derive the exact conditional joint and marginal MGFs and use them to derive the exact conditional marginal and joint density functions of the MLEs. These densities are used in turn to develop marginal and joint CIs for some quantities of interest. Finally, we consider the LBS distribution and formally show the different kinds of shapes of the probability density function (PDF) and the hazard function. We then derive the MLEs of the parameters and prove that they always exist and are unique. Next, we propose the MMEs, which can be used as initial values in the numerical computation of the MLEs. We also discuss the interval estimation of parameters. / Thesis / Doctor of Science (PhD)

The diploma thesis is written with a view to illustrate application of statistical methods describing progress of economical processes in company. The thesis is divided into two separated parts. First part focuses on theoretical pieces of knowledge about control charts and time series. Second part is composed from chapters that are focused on its practical usage. As simple application for control chart making is enclosed.

This diploma thesis deals with use of Shewhart Control Charts in quality control. The thesis describes the currently used process of quality control in the enterprise. Afterwards practical guidance for implementation of the statistical process control of the selected component and evaluation of capability is provided. An application for creating control charts and monitoring the quality of the product is included.