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Statements

Subject Item

dbr:Factorial_moment_measure

rdfs:label

Factorial moment measure

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.

dct:subject

dbc:Point_processes dbc:Spatial_analysis

dbo:wikiPageID

40990955

dbo:wikiPageRevisionID

1119714759

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dbr:Radon–Nikodym_derivative dbr:Derivative dbr:Taylor's_theorem dbr:Permutations dbr:Mathematical_model dbr:Random_variables dbr:Geology dbr:Stochastic_processes dbr:Probability dbr:Scientific dbr:Poisson_point_process dbr:Absolutely_continuous dbc:Point_processes dbr:Disjoint_sets dbr:Factorial_moment dbr:Multiplication dbr:Stochastic_geometry dbr:Integer dbr:Euclidean_space dbr:Mathematical_space dbr:Indicator_function dbr:Random dbr:Expected_value dbr:Space dbr:Point_process_notation dbr:Measurable_function dbr:Operator_(mathematics) dbr:Non-negative dbr:Tuples dbr:Biology dbr:Moment_measure dbr:Bounded_function dbr:Summation dbr:Function_(mathematics) dbr:Physics dbr:Spatial_statistics dbr:Cartesian_product dbr:Series_(mathematics) dbr:Average dbr:Engineering dbr:Abstraction_(mathematics) dbc:Spatial_analysis dbr:Functional_(mathematics) dbr:Lebesgue_measure dbr:Telecommunications dbr:Statistics dbr:Moment_(mathematics) dbr:Set_(mathematics) dbr:Point_process dbr:Time dbr:Random_measure dbr:Measure_(mathematics) dbr:Mathematical_objects dbr:Mathematical dbr:Dirac_measure dbr:Taylor_series dbr:Borel_set dbr:Correlation_and_dependence dbr:Point_(geometry) dbr:Correlation

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dbo: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.

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dbr:Quantity

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wikipedia-en:Factorial_moment_measure?oldid=1119714759&ns=0

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14684

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wikipedia-en:Factorial_moment_measure