Μοντέλα πιθανοτήτων για περιγραφή δεδομένων μεγάλου όγκου
Probability models for fitting big data
Over the last few decades, many scientists focused on the stochastic modeling of natural and social phenomena and arrived at the conclusion that many of them follow Power Law Distribution. This dissertation contains some brief definitions of the continuous PLD and presents in detail its properties. Furthermore, we present statistical methods for estimating the parameters of PLD along with Kolmogorov-Smirnov goodness-of-fit. Moreover, we compare PLD with other alternative fat-tailed distributions using likelihood ratios and also we describe some of them. Additionally, we use simulated data from PLD in order to find out which of the estimation methods gives best results and also which alternative distribution can describe better data from PLD. Finally, we present some applications of PLD and provide information on how one can apply estimating methods for the PLD parameters via several programming languages.