On the cases of Pareto and related distributions

학위논문(석사)--아주대학교 일반대학원 :수학과,2022. 21. Introduction 1 2. Preliminaries 4 2.1 Axioms of Probability 4 2.2 Random Variables 5 2.3 Distribution Functions 8 2.4 Probabilistic Methods 12 3 Pareto Distribution 15 3.1 Well-known examples 15 3.2 Data from Statistics Korea 16 4 Case Study 19 4.1 The size of human settlements 19 4.2 The size of traffic jam in Seoul 34MasterA Pareto distribution is a well-known distribution. It explains the cases of an uneven distribution. In this thesis, we discuss the Pareto distribution and other related distributions. Firstly, we study the Pareto distribution and provide some examples of the Pareto principle. Secondly, we analyse two data sets with interest. One is the size of human settlements in Korea. The other is the size of traffic jam in Seoul. We check that the Pareto distribution is an appropriate distribution to analyse the size of human settlements on a national scale. However, we find that the Pareto distribution is not able to analyse the size of traffic jam in Seoul. Accordingly, we analyse both the size of human settlements on smaller cases and the size of traffic jam in a big city with other distributions