• Corpus ID: 88513658

Two samples test for discrete power-law distributions

  title={Two samples test for discrete power-law distributions},
  author={Alessandro Bessi},
  journal={arXiv: Methodology},
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn from the same power-law distribution. 

Figures from this paper

From the power law to extreme value mixture distributions

Two extreme value mixture distributions are proposed, in one of which the power law is incorporated, without the need of pre-specifying the threshold, and the proposed distributions are shown to fit the data well, quantify the threshold uncertainty in a natural way, and satisfactorily answer whether the powerLaw is useful enough.

Speeding up lower bound estimation in powerlaw distributions

Two alternative methods are proposed with the aim to reduce the time required by the estimation procedure for powerlaw distributions based on the Kolmogorov-Smirnov distance with significantly better performance and accuracy than the traditional method.

Emotional contagion and group polarization: experimental evidence on facebook

Information, rumors, debates shape and reinforce the perception of reality and heavily impact public opinion. Indeed, the way in which individuals influence each other is one of the foundational

Debunking in a world of tribes

This work examines the effectiveness of debunking on Facebook through a quantitative analysis of 54 million users over a time span of five years, and confirms the existence of echo chambers where users interact primarily with either conspiracy-like or scientific pages.

Exploring Cognitive Dissonance on Social Media

After the event is revised, the performance of the original followers were abnormal, which is consistent with the existence of cognitive dissonance, and the followers’ attitude afterwards usually tended to maintain their previous behaviors.

Adversarial Attacks on Classification Models for Graphs

This work introduces the first study of adversarial attacks on attributed graphs, specifically focusing on models exploiting ideas of graph convolutions, and proposes an efficient algorithm Nettack exploiting incremental computations to cope with the underlying discrete domain.

Adversarial Attacks on Neural Networks for Graph Data

This work introduces the first study of adversarial attacks on attributed graphs, specifically focusing on models exploiting ideas of graph convolutions, and generates adversarial perturbations targeting the node's features and the graph structure, taking the dependencies between instances in account.

Adversarial Attacks on Graph Neural Networks

This work generates adversarial perturbations targeting the node’s features and the graph structure, thus, taking the dependencies between instances in account, and identifies important patterns of adversarial attacks on graph neural networks (GNNs) — a first step towards being able to detect adversarial attack on GNNs.

Towards Revealing Parallel Adversarial Attack on Politician Socialnet of Graph Structure

A parallel adversarial attack framework on node classification is proposed, which redesign new loss function and objective function for nonconstraint and constraint perturbations, respectively, and integrates node filtering-based P-FGA and P-NETTACK in a unified framework.

All You Need Is Low (Rank): Defending Against Adversarial Attacks on Graphs

This paper explores the properties of Nettack perturbations and proposes LowBlow, a low-rank adversarial attack which is able to affect the classification performance of both GCN and tensor-based node embeddings and it is shown that the low- rank attack is noticeable and making it unnoticeable results in a high-rank attack.



Power-Law Distributions in Empirical Data

This work proposes a principled statistical framework for discerning and quantifying power-law behavior in empirical data by combining maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios.

Evaluating Kolmogorov's distribution

Kolmogorov's goodness-of-fit measure, Dn , for a sample CDF has consistently been set aside for methods such as the D+n or D-n of Smirnov, primarily, it seems, because of the difficulty of computing

Inference and Asymptotics

Introduction Preliminaries Some general concepts First order theory Higher order theory:preliminaries Mathematical basis of higher order theory Higher order theory: likelihood combinants higher order

All of Statistics: A Concise Course in Statistical Inference

This book covers a much wider range of topics than a typical introductory text on mathematical statistics, and includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses.

Practical Nonparametric Statistics

This book is aimed at graduate students in statistics or mathematics, and practicing statisticians, and requires proficiency in advanced calculus, and can serve as a very good reference on the exciting topic of wavelets.