Bimodální rozdělení
Bimodal distributions
rigorous thesis (RECOGNIZED)

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http://hdl.handle.net/20.500.11956/24703Identifiers
Study Information System: 73828
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- Kvalifikační práce [9699]
Author
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
10. 6. 2009
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
Czech
Grade
Recognized
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.