BAH, A. Statistická analýza cenzorovaných dat [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.

Posudek vedoucího

Fusek, Michal

The thesis deals with statistical methods for Type I left-censored data with the Weibull, lognormal and gamma distributions. Chapter 2 describes differences between the censored and truncated samples together with descriptions of some types of censoring. Chapter 3 describes Type I left-censored models for the Weibull, lognormal and gamma distributions. Unknown parameters are estimated using the maximum likelihood method. The estimators’ performance is assessed using simulations. The described methods are applied to real data in Chapter 4. I would like to mention that the author was actively working on the thesis during the whole academic year and also during the summer holidays. In our regular meetings I discovered that the topic of the thesis was quite difficult for him because of his limited knowledge of Matlab and probability and statistics in general. Eventually he gained the essential knowledge and was able to apply it with my assistance in the problems connected with the topic of the thesis. He also managed to put together the Matlab codes for simulations and the real data application. Despite the fact that the thesis contains some mistakes and language style imperfections (spaces, capital letters), all the main goals of the thesis have been achieved and I recommend the thesis for defense with the overall classification C.

Posudek oponenta

Hlavičková, Irena

The submitted thesis studies the statistical analysis of data sets containing censored values.  Although the work is quite interesting and the desribed methods have a wide range of applications, there are some imperfections. There are some misprints, e.g. in the usage of small and capital letters. In chapter 2.3, the ordered values are denoted as X_{i:n}, ..., meanwhile in futher chapters they are denoted as X_(i). In chapter 3. 2. 1, the shape parametr of Weibull distribution is denoted as theta in the formula for pdf but as k in the description of the properties of this distribution. The statement that for k=1 is cdf linear, is false. In formula (3.7), p. 35, there should not be the exponent N_i. In chapter 3.2.5, there is an error in the definition of the incomplete gamma function. Partial derivatives of (3.10) contain functions psi^0(k), Psi(k) and Psi(1,k) which were not defined. In the real data application, it may not be clear to the reader what exactly was measured, where the data came from. Despite the mentioned shortcomings, I recommend the thesis for defence with a grade of C.

eVSKP id 162460