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In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables.

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rdfs:label	Factorial moment measure (en)
rdfs:comment	In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables. (en)
dct:subject	Spatial analysis Point processes
Wikipage page ID	40990955 (xsd:integer)
Wikipage revision ID	1119714759 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Random measure Biology Bounded function Derivative Permutations Correlation Correlation Measure (mathematics) Operator (mathematics) Engineering Function (mathematics) Functional (mathematics) Geology Moment (mathematics) Multiplication Statistics Stochastic processes Physics Point (geometry) Space Measurable function Spatial analysis Time Disjoint sets Lebesgue measure Euclidean space Expected value Factorial moment Absolutely continuous Non-negative Radon–Nikodym derivative Probability Random Taylor's theorem Taylor series Telecommunications Abstraction (mathematics) Point processes Summation Dirac measure Average Borel set Poisson point process Indicator function Integer Random variables Set (mathematics) Mathematical model Series (mathematics) Point process Moment measure Stochastic geometry Point process notation Mathematical Mathematical objects Tuples Scientific Spatial statistics Mathematical space
sameAs	Factorial moment measure Factorial moment measure Factorial moment measure Factorial moment measure
dbp:wikiPageUsesTemplate	dbt:ProbabilityTopics dbt:Main dbt:Notelist
has abstract	In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables. The first factorial moment measure of a point process coincides with its first moment measure or intensity measure, which gives the expected or average number of points of the point process located in some region of space. In general, if the number of points in some region is considered as a random variable, then the moment factorial measure of this region is the factorial moment of this random variable. Factorial moment measures completely characterize a wide class of point processes, which means they can be used to uniquely identify a point process. If a factorial moment measure is absolutely continuous, then with respect to the Lebesgue measure it is said to have a density (which is a generalized form of a derivative), and this density is known by a number of names such as factorial moment density and product density, as well as coincidence density, joint intensity, correlation function or multivariate frequency spectrum The first and second factorial moment densities of a point process are used in the definition of the pair correlation function, which gives a way to statistically quantify the strength of interaction or correlation between points of a point process. Factorial moment measures serve as useful tools in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications. (en)
gold:hypernym	Quantity
prov:wasDerivedFrom	wikipedia-en:Factorial_moment_measure?oldid=1119714759&ns=0
page length (characters) of wiki page	14684 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Factorial_moment_measure
is Link from a Wikipage to another Wikipage of	Spherical contact distribution function Determinantal point process Nathalie Eisenbaum Haya Kaspi Factorial moment Poisson point process Nearest neighbour distribution Campbell's theorem (probability) Moment measure Stochastic geometry
is foaf:primaryTopic of	wikipedia-en:Factorial_moment_measure

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