Power law distributions, self-organizing behavior and popularity


Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Graduate School of Informatics, Cognitive Science, Turkey

Approval Date: 2015

Student: DUYGU GÖZDE NASUHBEYOĞLU

Co-Supervisor: HÜSEYİN CEM BOZŞAHİN, CENGİZ ACARTÜRK

Abstract:

Zipf (1949) formulated Zipf’s Law, which is based on mathematical statistics and is named after him, for many types of empirical data collected for analyzing physical or social sciences. Zipf’s Law is a kind of Power Law probability distributions. One can do a Kolmogorov-Smirnov test to check whether there is goodness of fit to the hypothesized Power Law distribution and then exponential and lognormal distributions can be compared with the log likelihood ratio of the Power Law distribution to test whether an empirical data set applies to Zipf’s law (Clauset et al., 2009). This method forms the basis of the method used in this thesis. The hypothesis of this thesis is "People’s behavior’s e ect on popularity fits a Power Law distribution". To investigate this hypothesis, random top (popular) songs on iTunes have been selected and their YouTube ratings were collected every day for more than one month. Results were expected to show that the frequency of likes or dislikes increase every day and for songs that are liked or disliked more would be liked or disliked more. Also, in order to understand how something so random can become so popular, Internet Mahir’s website’s (Çağrı, 1999) Google search engine statistics have been analyzed. This thesis is to find out whether popularity is aff ected by other people’s behaviour.