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Comparison of exact and asymptotic tests
Rusnáková, Viktória ; Hlubinka, Daniel (advisor) ; Došlá, Šárka (referee)
Nazev prace: Porovnani pfesnych a asymptotickych testu Autor: Viktoria Rusnakova Katedra: Katcdra pravdepodobnosti a matematicke statistiky Vedouci bakalafske prace: Doc. RNDr. Daniel Hlubinka, Ph.D. e-mail vedouciho: hlubinka(Q)karlin.mff.cuni.cz Abstrakt: Predlozena praca sa zaobera testami o parametroch binomickeho. Poiaso novho a cxponencialneho rozdclenia. Ciol'om prace je porovnat! presne znahodneiie testy a testy asymptoticke, zalozcne na centralnej limitnej veto a zalozcne na metode maximalnej vierohodnosti. V prvej, teoretickej casti su uvedene potrebne vety a tvrdcnia, na zaklado ktorych su zostrojenc priklady pro dane rozdclenia. Druha, prakticka cast' je venovana pocitacovym simulaciarn obojstrannych testov na hlacline vyznamnosti 5 %. Vysledky siraulacii su uvedene na prilozenom CD. Klfcova slova: kriticka funkcia, znahodneny test, asymptoticky test Title: Comparison of exact and asymptotic tests Author: Viktoria Rusnakova Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Daniel Hlubinka, Ph.D. Supervisor's e-mail address: hlubinkaykarhn.mff.cuin.cz Abstract: The presented work deals with tests about parameters of binomial, Poisson and exponencial distribution. The aim of this work is to compare exact randomized tests and asymptotic tests based on central...
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Bimodal distributions
Došlá, Šárka ; Anděl, Jiří (advisor) ; Dupač, Václav (referee)
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1;...;N is bimodal.
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Bimodal distributions
Došlá, Šárka
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1....N is bimodal.
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Comparison of exact and asymptotic tests
Rusnáková, Viktória ; Došlá, Šárka (referee) ; Hlubinka, Daniel (advisor)
Nazev prace: Porovnani pfesnych a asymptotickych testu Autor: Viktoria Rusnakova Katedra: Katcdra pravdepodobnosti a matematicke statistiky Vedouci bakalafske prace: Doc. RNDr. Daniel Hlubinka, Ph.D. e-mail vedouciho: hlubinka(Q)karlin.mff.cuni.cz Abstrakt: Predlozena praca sa zaobera testami o parametroch binomickeho. Poiaso novho a cxponencialneho rozdclenia. Ciol'om prace je porovnat! presne znahodneiie testy a testy asymptoticke, zalozcne na centralnej limitnej veto a zalozcne na metode maximalnej vierohodnosti. V prvej, teoretickej casti su uvedene potrebne vety a tvrdcnia, na zaklado ktorych su zostrojenc priklady pro dane rozdclenia. Druha, prakticka cast' je venovana pocitacovym simulaciarn obojstrannych testov na hlacline vyznamnosti 5 %. Vysledky siraulacii su uvedene na prilozenom CD. Klfcova slova: kriticka funkcia, znahodneny test, asymptoticky test Title: Comparison of exact and asymptotic tests Author: Viktoria Rusnakova Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Daniel Hlubinka, Ph.D. Supervisor's e-mail address: hlubinkaykarhn.mff.cuin.cz Abstract: The presented work deals with tests about parameters of binomial, Poisson and exponencial distribution. The aim of this work is to compare exact randomized tests and asymptotic tests based on central...
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Bimodal distributions
Došlá, Šárka
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1....N is bimodal.
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Bimodal distributions
Došlá, Šárka ; Dupač, Václav (referee) ; Anděl, Jiří (advisor)
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1;...;N is bimodal.
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