Štatistické testy normality
Statistical tests of normality
Statistické testy normality
bachelor thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/184327Identifiers
Study Information System: 250752
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- Kvalifikační práce [11214]
Author
Advisor
Referee
Omelka, Marek
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
General Mathematics
Department
Department of Probability and Mathematical Statistics
Date of defense
7. 9. 2023
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
Slovak
Grade
Good
Keywords (Czech)
statistický test|normálne rozdelenie|Gaussovo rozdelenieKeywords (English)
statistical test|normal distribution|Gaussian distributionCieľom tejto práce je predstaviť známe, v praxi používané testy normality a porovnať ich. Prvá kapitola pozostáva zo základných pojmov a vlastnosti normálneho rozdelenia. V druhej kapitole je spracovaných 6 testov normality, konkréte Kolmogorov-Smirnov, Lilliefors, Shapiro-Wilk, Anderson-Darling, D'Agostino-Pearson a Jarque-Bera. Pre každý test je okrem iného uvedená testová štatistika a tvar kriticého oboru. Tretia kapitola s empirickou štúdiou obsahuje dve časti. V prvej časti je stručne vysvetlený charakter štúdie a empiricky skontrolovaná deklarovaná hladina testov. V druhej časti je empiricky porovnaná sila testov proti rôznym alternatívam a diskusia výsledkov. 1
The aim of this paper is to present the well-known normality tests used in practice and to compare them. The first chapter consists of the basic concepts and properties of the nor- mal distribution. In the second chapter 6 normality tests are treated, namely Kolmogorov- Smirnov, Lilliefors, Shapiro-Wilk, Anderson-Darling, D'Agostino-Pearson and Jarque- Bera. For each test, test statistic and shape of critical region are given, among others. The third chapter, with empirical study, contains two parts. In the first part, nature of the study is briefly explained and level of significance declared by tests is empirically-checked. In the second part, power of tests is empirically compared against various alternatives and the results are discussed. 1