Related papers: Long-tailed distributions of inter-event times as …
Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human…
Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…
We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed…
In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…
Response latency -- the time taken to initiate or complete an action or task -- is one of the principal measures used to investigate the mechanisms subserving human and animal cognitive processes. The right tails of response latency…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively…
Inspired by previous works on human dynamics, we collect the temporal statistics of the article creation by three Western scientists and an Eastern writer. We investigate the distributions of the time intervals between the creations of…
In this work, we introduce a new methodology for inferring the interaction structure of discrete valued time series which are Poisson distributed. While most related methods are premised on continuous state stochastic processes, in fact,…
Similar to charitable giving in real world, donation behaviors play an important role in the complex interactions among individuals in virtual worlds. However, it is not clear if the donation process is random or not. We investigate this…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
Motivated by a host of empirical evidences revealing the bursty character of human dynamics, we develop a model of human activity based on successive switching between an hesitation state and a decision-realization state, with residency…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…