The Poisson-Dirichlet Distribution and Sampling Formulas

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Title: The Poisson-Dirichlet Distribution and Sampling Formulas
Author: Maunu, Joonas
Contributor: University of Helsinki, Faculty of Science
Publisher: Helsingin yliopisto
Date: 2019
Language: eng
Thesis level: master's thesis
Discipline: Soveltava matematiikka
Abstract: This thesis is based on Masanao Aoki's idea to use Poisson-Dirichlet sampling formulas and models on economical phenomena. He suggested that these models could be used for innovations. Inspired by that, the subject of this thesis' research is employment in the USA. The dataset is relatively comprehensive since economy of the USA is large enough. We use both, the one-parameter Ewens Sampling Formula and its extension, the two-parameter Pitman sampling formula, in simulations. Both of them are used to see how the complexity of model a ects on the result. Sampling formulas are e ective to use since they are used only on the latest state of the employment. By exchangeability, we are able to simulate with urn-type construction and result in a similar outcome as the state of the real employment distribution. The model makes many simpli cations and doesn't concern about speci c elds of employment. It treats them all equally. Therefore it can be thought as a macroeconomic model and could be used as boundaries for more speci c models. We use also Monte Carlo to simulate larger datasets than what we get with the urn-type construc- tion. With Monte Carlo and urn-type constructed simulations we test the probability of original employment distribution.

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