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Normality test of the gene expression data
Shokirov, Bobosharif ; Klebanov, Lev (advisor) ; Hušková, Marie (referee) ; Kalina, Jan (referee)
This thesis deals with a test of normality of gene expressions data. Based on characterization theorems of the normal distribution, the test of normality is replaced by a test of spherical uniformity. Due to strong correlations between the gene expression data, the normality test is conducted with $\delta$ sequences. A new characterization theorem of the normal distribution is proven. Based on that, the normality test is conducted using Kolmogorov's test statistic. The obtained characterization results for the normal distribution are extended to the complete type of distributions and based on that, a test is conducted to verify whether the distributions of the two data sets of the gene expressions belong to the same type. Powered by TCPDF (www.tcpdf.org)
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Normality test of the gene expression data
Shokirov, Bobosharif ; Klebanov, Lev (advisor) ; Hušková, Marie (referee) ; Kalina, Jan (referee)
This thesis deals with a test of normality of gene expressions data. Based on characterization theorems of the normal distribution, the test of normality is replaced by a test of spherical uniformity. Due to strong correlations between the gene expression data, the normality test is conducted with $\delta$ sequences. A new characterization theorem of the normal distribution is proven. Based on that, the normality test is conducted using Kolmogorov's test statistic. The obtained characterization results for the normal distribution are extended to the complete type of distributions and based on that, a test is conducted to verify whether the distributions of the two data sets of the gene expressions belong to the same type. Powered by TCPDF (www.tcpdf.org)
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Shapiro-Wilk test of normality
Malíková, Kateřina ; Komárek, Arnošt (advisor) ; Zvára, Karel (referee)
In this work we introduce Shapiro-Wilk normality test testing examined statistical sampling. At first, we state the basic information about the normal distribution. Further, we describe the test and we derive the shape of the test statistic W and some of its analytical properties, including two moments and the maximum and minimum allowable values that it may take. We also find some approximations of various coefficients used for calculations and evaluation of the test and also the estimate of the distribution of the test statistics of Shapiro-Wilk test. In conclusion, we show an example of testing and method of implementation in computer programs.
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