statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, 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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

of an event.Lambiotte, R. (2013.) "Burstiness and Spreading on Temporal Networks", University of Namur. One measure 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 counting process. It was originally used to measure the Fano noise in ion detectors. It is named after Ugo Fano, an Itali ...

—a ratio between the

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

and

mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...

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

natural disaster A natural disaster is the very harmful impact on a society or community brought by natural phenomenon or Hazard#Natural hazard, hazard. Some examples of natural hazards include avalanches, droughts, earthquakes, floods, heat waves, landslides ...

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 Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ...

email Electronic mail (usually shortened to email; alternatively hyphenated e-mail) is a method of transmitting and receiving Digital media, digital messages using electronics, electronic devices over a computer network. It was conceived in the ...

network traffic or vehicular traffic. Burstiness is, in part, due to changes in the

probability distribution In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...

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 :

\mathrm(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 models Applied statistics

Burstiness score

See also

References