statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, burstiness is the intermittent increases and decreases in activity or

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

of an event.Lambiotte, R. (2013.) "Burstiness and Spreading on Temporal Networks", University of Namur. One of measures of burstiness is the

Fano factor In statistics, the Fano factor, like the coefficient of variation, is a measure of the statistical dispersion, dispersion of a probability distribution of a Fano noise. It is named after Ugo Fano, an Italian American physicist. The Fano factor is d ...

—a ratio between the

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...

and

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the '' ari ...

of counts. Burstiness is observable in natural phenomena, such as

natural disaster A natural disaster is "the negative impact following an actual occurrence of natural hazard in the event that it significantly harms a community". A natural disaster can cause loss of life or damage property, and typically leaves some econ ...

s, or other phenomena, such as

network Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics ...

data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...

email Electronic mail (email or e-mail) is a method of exchanging messages ("mail") between people using electronic devices. Email was thus conceived as the electronic ( digital) version of, or counterpart to, mail, at a time when "mail" meant ...

network traffic or vehicular traffic. Burstiness is, in part, due to changes in the probability distribution of inter-event times. Distributions of bursty processes or events are characterised by heavy, or fat, tails. Burstiness of inter-contact time between nodes in a time-varying network can decidedly slow spreading processes over the network. This is of great interest for studying the spread of information and disease.

Burstiness Score

One relatively simple measure of burstiness is burstiness score. The burstiness score of a subset

t

of time period

T

relative to an event

e

is a measure of how often

e

appears in

t

compared to its occurrences in

T

. It is defined by :

Burst(e, t) = \left (\frac - \frac\right )

Where

E_t

is the total number of occurrences of event

e

in subset

t

and

E

is the total number of occurrences of

e

T

. Burstiness score can be used to determine if

t

is a "bursty period" relative to

e

. A positive score says that

e

occurs more often during subset

t

than over total time

T

, making

t

a bursty period. A negative score implies otherwise. A. Hoonlor et al. (2013).
An Evolution of Computer Science Research
, ''Communications of the ACM'', 56(10):79

References

{{Reflist Markov processes Applied statistics

Burstiness Score

See also

References