Related papers: Long-tailed distributions of inter-event times as …
Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. A basic assumption embedded in the previous analyses on human dynamics is that its temporal statistics are…
Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, and this property impacts contagion and other dynamical processes on networks. We theoretically show that distributions of…
Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the…
Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…
The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in…
Minimum message length is a general Bayesian principle for model selection and parameter estimation that is based on information theory. This paper applies the minimum message length principle to a small-sample model selection problem…
Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…
We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
We continue our study of exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low temperature plus phase of the Ising model, we prove exponential laws with error bounds for occurrence,…
Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…
We notice signatures of extreme events-like behavior in a laser based Ikeda map. The trajectory of the system occasionally travels a large distance away from the bounded chaotic region, which appears as intermittent spiking events in the…
In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
Temporal sequences of discrete events that describe natural and social processes are often driven by non-Poisson dynamics. In addition to a heavy-tailed interevent time distribution, which primarily captures the deviation from a Poisson…
A diverse variety of processes --- including recurrent disease episodes, neuron firing, and communication patterns among humans --- can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event…
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between…
Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…