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Infinite products
Kudrnáč, Vojtěch ; Rokyta, Mirko (advisor) ; Černý, Robert (referee)
This paper offers a brief insight into the basic theory of convergence of the infinite products of real or complex sequences. Then it focuses mainly on the possibilities of developing some selected functions into the form of infinite product and on the corollaries and utilizations of being familiar with these. Purpose of the paper is not to prove the existence of infinite products for functions with certain characteristics in general, but rather to derive specific formulas and prove their validity. The attention is paid to those elementary functions which are derived from the exponential function, especially the sinus function, the nonelementary functions mentioned are the gamma and the zeta function. The text should be understandable even for a person, who has never came upon infinite products before.
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Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
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Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
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Infinite products
Kudrnáč, Vojtěch ; Rokyta, Mirko (advisor) ; Černý, Robert (referee)
This paper offers a brief insight into the basic theory of convergence of the infinite products of real or complex sequences. Then it focuses mainly on the possibilities of developing some selected functions into the form of infinite product and on the corollaries and utilizations of being familiar with these. Purpose of the paper is not to prove the existence of infinite products for functions with certain characteristics in general, but rather to derive specific formulas and prove their validity. The attention is paid to those elementary functions which are derived from the exponential function, especially the sinus function, the nonelementary functions mentioned are the gamma and the zeta function. The text should be understandable even for a person, who has never came upon infinite products before.
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