KONEČNÁ, T. Modely s Weibullovým rozdělením [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2017.

Posudek vedoucího

Hübnerová, Zuzana

Bc. Konečná was working on the topic carefully and with her fullest commitment. Studying the topic required in-depth understanding of many papers and monographies. Bc. Konečná found some of the sources on her own initiative. For the actual program implementation of obtained results the author had to learn R coding from scratch. She used GAMS software actively as well. In the thesis, I particularly value the comparison of several variants of the method of quantiles for parameter estimation of the two-parameter Weibull distribution. The derivation of the asymptotic distribution of the parameter estimates by some of the variants of the method of quantiles makes a great contribution. The maximum likelihood method (also studied in the thesis) requires iterative seeking for the estimates which can be initiated in the parameter estimate obtained by suitable variant of the method of quantiles. Next, Bc. Konečná derived the asymptotic distribution of the maximum likelihood estimates successfully. And so it is possible to compare all methods of parameter estimation which is also presented in the thesis. Also the estimates based on the least squares method applied in the Weibull probability plot are derived newly. Studied methods of parameter estimation are compared by simulations in the thesis as well. Possible goodness of fit tests of the Weibull distribution were studied carefully and coded in R. The derivations of the maximum likelihood estimates and tests on parameters in the one-way ANOVA type Weibull models required extensive diligence and concentration. Bc. Konečná coped that challenge nicely. During the preparation of the thesis, it became clear that the language level of the text needs a special attention. I believe, this experience leads to scientific texts with a better language level than you can see in some parts of the diploma thesis. I'm convinced that the created R programs will be of advantage for other statisticians working with Weibull models. I also believe that the obtained theoretical results will initiate a successful paper in a scientific journal.

Posudek oponenta

Karpíšek, Zdeněk

Text předložené diplomové práce je přesný a stručný s ohledem na diskutované modely a metody. Diplomová práce prokazuje, že autorka výborně zvládla stochastické modelování v dané oblasti problémů s odhady parametrů Weibullova rozdělení. Získané výsledky softwarově implementovala a také aplikovala. Práce demonstruje kreativitu autorky, její schopnost vytvářet přesné závěry a přinést nové pohledy na aplikace získaných výsledků. Diplomová práce neobsahuje chyby v popisu modelů a metod, a oceňuji, že je napsaná velmi dobrou angličtinou. Jsou v ní jen menší a zanedbatelné nepřesnosti (pravděpodobně způsobený snahou po stručnosti) a sporadické překlepy, které však nesnižují významně celkově výbornou úroveň práce. Editace textu a vzorců je v editoru TeX, tabulky a obrázky jsou dostatečně kvalitní a vhodně doplňuji text. Cíle diplomové práce byly zaměřené na řešení moderních a velmi důležitých problémů. Práce tyto cíle zcela splňuje. Autorský přístup a získané výsledky jsou rigorózní. Popisovaná řešení mají význam nejen pro praktické aplikace, ale také poskytují zajímavé impulzy pro řešení teoretických problémů. The text of the submitted master´s thesis is accurate and concise enough with respect to the discussed models and methods. The text shows that the author very well mastered the modeling and solution challenges related to the studied estimation problems. The obtained results were implemented in software and also applied. The author demonstrated erudition, the ability to draw rigorous conclusions and brought new insights for the application of the obtained results. The master´s thesis does not contain errors in the description of the models and methods and I appreciate that it is written in very good English. There are only minor and negligible inaccuracies (probably caused by the desire for brevity) and the sporadic typos, which, however, do not reduce significantly the overall high level of work. The setting of text and formulas is in the editor TeX, and tables and pictures are of good quality and suitably complement the text. The objectives of the master´s thesis focused on solving modern and very important challenges. The dissertation has fulfilled these goals completely. The author’s approach and the obtained results are rigorous. The described solutions have importance not only for practical applications but also provide interesting impulses for the solution of theoretical problems.

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