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Jakob Bergman
Studierektor, Statistiska institutionen
![Porträtt av Jakob Bergman. Foto.](/sites/ehl.lu.se/files/styles/lu_personal_page_desktop/public/2024-02/JakobBergman.jpg.webp?itok=sf6g3DpI)
On Bicompositional Correlation
Författare
Summary, in English
We introduce a generalization of the Dirichlet distribution to simultaneously describe two compositions, i.e. a bicompositional Dirichlet distribution. The covariation between the two compositions is modelled by a parameter γ. If γ=0, then the two compositions are independent. For compositions with two components, we prove for which γ the distribution exists. We also give expressions for the normalization constant and other properties, such as moments, marginal and conditional distributions. For compositions that have more than two components, we present expressions for the normalization constant and other properties for all non-negative integers γ. We also present a method for generating random numbers from the distribution for all γ≥0 and for some γ<0 if the compositions have two components. The method is based on the rejection method.
We use this bicompositional distribution and a general measure of correlation based on the concept of information gain to calculate a measure of correlation between two compositions for a large number of models. Finally we present an estimator of the general measure of correlation. We compare two suggestions of confidence intervals for the general measure of correlation.
Avdelning/ar
- Statistiska institutionen
Publiceringsår
2010
Språk
Engelska
Publikation/Tidskrift/Serie
Doctoral Theses in Statistics
Fulltext
- Available as PDF - 655 kB
- Available as PDF - 250 kB
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Dokumenttyp
Doktorsavhandling
Ämne
- Probability Theory and Statistics
Nyckelord
- Joint correlation coefficient
- Empirical confidence coefficient
- Dirichlet distribution
- Correlation
- Composition
- Compositional data
- Random variate generation
- Simplex
Aktiv
Published
Handledare
- Björn Holmquist
- Krzysztof Nowicki
ISBN/ISSN/Övrigt
- ISSN: 1651-7938
- ISBN: 978-91-628-8028-6
Försvarsdatum
16 april 2010
Försvarstid
10:15
Försvarsplats
EC3:207, Holger Crafoords Ekonomicentrum
Opponent
- Peter Guttorp (Professor)