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When applying statistical methods for analyzing data, with normality as an assumption there are different procedures of determining if a sample is drawn from a normally distributed population. Because normality is such a central assumption, the reliability of the procedures is of most importance. Much research focus on how good formal tests of normality are, while the performance of statisticians when using graphical methods are far less examined. Therefore, the aim of the study was to empirically examine how good students in statistics are at assessing if samples are drawn from normally distributed populations through graphical methods, done by a web survey. The results of the study indicate that the students distinctly get better at accurately determining normality in data drawn from a normally distributed population when the sample size increases. Further, the students are very good at accurately rejecting normality of data when the sample is drawn from a symmetrical non-normal population and fairly good when the sample is drawn from an asymmetrical distribution. In comparison to some common formal tests of normality, the students' performance is superior at accurately rejecting normality for small sample sizes and inferior for large, when drawn from a non-normal population.

This paper presents a stability analysis of the sensor data which is collected by QTAGG from alarge ocean going ship and using the stability results, introduces some information about howthe measurements that come from the sensors can be improved and how reliable they are. In thetheoretical part, some background information is given mainly based on British Standard(BS)ISO 19030 which was published in November, 2016. This source basically includes someinformation about the measurement of changes in hull and propeller performance of a vessel.Using the theoretical information, in the implementation part, the necessary methods areimplemented in python programming language on a real life data set of a vessel which is givenfrom QTAGG company. To measure the stability of the parameters in the data, we loosenthe filters of the parameters and observe how they respond to the technical changes. In orderto understand how loosen the filters can be made, a reference speed-power curve is createdby using a curve fitting method, and after creating a performance indicator by utilizing thereference curve, Anderson-Darling and Shapiro-Wilk tests are used to measure the stability ofthe performance indicator. Besides these numerical tests, some visual methods such as Q-Qplot and histogram plot are also used in this process. Finally, we could provide stability resultsby using both our theoretical knowledge and the practical implementation.

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 thesis deals with the visualization of biomedical data in MATLAB environment. The thesis contains following statistical methods and their descriptions: P-P plot, Q-Q plot, histogram, box plot, kernel denstity estimation, scatter plot and several time series metrics. Some functions are programmed from buil-in functions of MATLAB and others using external functions, which are changed to fit to this thesis’s purpose. First part of the thesis conserns theoretical background, whereas the second part conserns practical programmed realizations of mentioned functions. The program contains a graphical user interface - GUI, which the thesis describes in detail. The purpose of the GUI is to ensure ease of use and also data processing. The output graphs of GUI are shown in chapter 5. The last part deals with the possible extensions of the program.

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