IBUKUN, M. Modely s Touchardovým rozdělením [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2021.
In my opinion, Mr. Ibukun learned a lot while writing his thesis. I was impressed by how systematically he approached learning R. However, I did not like the stress of finalizing the thesis. There might be several reasons for that but I hope the experience will help to avoid this in the future. Most of the studied properties of the Touchard distribution in Chapter 3 are given in the paper by Matsushita et al, 2018. However, I could observe, that Mr. Ibukun strived to understand what he presents in the thesis. So he derived the properties on his own with some smaller help. Nevertheless, the plots of the ratio of void probabilities to compare Touchard and Poisson distribution are novel. Also new plots of skewness and kurtosis show for which values of parameters we might expect the values of those central moments to reach the normal limit. I value the results in Chapter 6 which show the properties of tests on equality of two independent samples from the Touchard distribution with known parameter delta. On the other hand, I regret that the comparison by simulations was done for a limited set of values and the plots don't allow the visual alignment.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | B | ||
| Postup a rozsah řešení, adekvátnost použitých metod | C | ||
| Vlastní přínos a originalita | C | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | B | ||
| Využitelnost výsledků v praxi nebo teorii | B | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | B | ||
| Samostatnost studenta při zpracování tématu | D |
The diploma thesis is focused on the study of Touchard discrete probability distribution, which is a generalization of the Poisson distribution, and was first published in 2018. The aim was to describe this distribution, its properties and compare methods of generalized linear models and maximum likelihood. Another task of the graduate was the implementation and PC realization of these methods on simulated statistical samples. In Chapter 2 the author presents a class of exponential distributions, in Chapter 3 the author describes Touchard probability distribution, in Chapter 4 the author deals with linear regression models, in Chapter 4 testing statistical hypotheses and in Chapter 5 comparing two selections from the distribution, including simulation calculating of power test. In the appendix, the author presents his R - codes for calculations of powers tests, dependence of variance and mean value, kurtosis, ratio of the probabilities of zeros, and skewness. The graduate fulfilled the assignment of the diploma thesis in full. The work brings new knowledges about the properties of the Touchard probability distribution. The obtained results and implementation of methods in R language are undoubtedly beneficial for the application of the described inferential statistical methods in practice. The work is clearly and comprehensibly written and equipped with the necessary pictures. Formulation inaccuracies and other ways of quoting literary sources are not essential. I recommend the author to publish the obtained results.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | B | ||
| Vlastní přínos a originalita | A | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | B | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | B |
eVSKP id 133319