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- Campbells_theorem_(probability) abstract "In probability theory and statistics, Campell's theorem or the Campbell-Hardy theorem can refer to a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the intensity measure of the point process, which allows for the calculation of expected value and variance of the random sum. One version of the theorem specifically relates to the Poisson point process and gives a method for calculating moments as well as Laplace functionals of the process.Another result by the name of Campell's theorem, but also known as Campbell's formula, entails an integral equation for the aforementioned sum over a general point process, and not necessarily a Poisson point process. There also exist equations involving moment measures and factorial moment measures that are considered versions of Campbell's formula. All these results are employed in probability and statistics with a particular importance in the related fields of point processes, stochastic geometry and continuum percolation theory, spatial statistics.The theorem's name stems from the work by Norman R. Campbell on theormionic noise, also known as shot noise, in vacuum tubes, which was partly inspired by the work of Ernest Rutherford and Hans Geiger on alpha particle detection, where the Poisson point process arose as a solution to a family of differential equations by Harry Bateman. In Campbell's work, he presents the moments and generating functions of the random sum of a Poisson process on the real line, but remarks that the main mathematical argument was due to G. H. Hardy, which has inspired the result to be sometimes called the Campbell-Hardy theorem.".
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- Campbells_theorem_(probability) wikiPageWikiLink Absolute_convergence.
- Campbells_theorem_(probability) wikiPageWikiLink Absolutely_convergent.
- Campbells_theorem_(probability) wikiPageWikiLink Almost_surely.
- Campbells_theorem_(probability) wikiPageWikiLink Alpha_particle.
- Campbells_theorem_(probability) wikiPageWikiLink Borel_set.
- Campbells_theorem_(probability) wikiPageWikiLink Category:Probability_theorems.
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- Campbells_theorem_(probability) wikiPageWikiLink Continuum_percolation_theory.
- Campbells_theorem_(probability) wikiPageWikiLink Convergence_(mathematics).
- Campbells_theorem_(probability) wikiPageWikiLink Counting_measure.
- Campbells_theorem_(probability) wikiPageWikiLink Equation.
- Campbells_theorem_(probability) wikiPageWikiLink Ernest_Rutherford.
- Campbells_theorem_(probability) wikiPageWikiLink Euclidean_space.
- Campbells_theorem_(probability) wikiPageWikiLink Expected_value.
- Campbells_theorem_(probability) wikiPageWikiLink Factorial_moment_measure.
- Campbells_theorem_(probability) wikiPageWikiLink Fubinis_theorem.
- Campbells_theorem_(probability) wikiPageWikiLink Function_(mathematics).
- Campbells_theorem_(probability) wikiPageWikiLink G._H._Hardy.
- Campbells_theorem_(probability) wikiPageWikiLink Hans_Geiger.
- Campbells_theorem_(probability) wikiPageWikiLink Harry_Bateman.
- Campbells_theorem_(probability) wikiPageWikiLink If_and_only_if.
- Campbells_theorem_(probability) wikiPageWikiLink Imaginary_number.
- Campbells_theorem_(probability) wikiPageWikiLink Integral.
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- Campbells_theorem_(probability) wikiPageWikiLink Measure_(mathematics).
- Campbells_theorem_(probability) wikiPageWikiLink Moment-generating_function.
- Campbells_theorem_(probability) wikiPageWikiLink Moment_(mathematics).
- Campbells_theorem_(probability) wikiPageWikiLink Moment_measure.
- Campbells_theorem_(probability) wikiPageWikiLink Norman_Robert_Campbell.
- Campbells_theorem_(probability) wikiPageWikiLink Point_process.
- Campbells_theorem_(probability) wikiPageWikiLink Point_process_notation.
- Campbells_theorem_(probability) wikiPageWikiLink Poisson_point_process.
- Campbells_theorem_(probability) wikiPageWikiLink Probability_theory.
- Campbells_theorem_(probability) wikiPageWikiLink Random.
- Campbells_theorem_(probability) wikiPageWikiLink Randomness.
- Campbells_theorem_(probability) wikiPageWikiLink Range_(mathematics).
- Campbells_theorem_(probability) wikiPageWikiLink Real_line.
- Campbells_theorem_(probability) wikiPageWikiLink Shot_noise.
- Campbells_theorem_(probability) wikiPageWikiLink Spatial_analysis.
- Campbells_theorem_(probability) wikiPageWikiLink Spatial_statistics.
- Campbells_theorem_(probability) wikiPageWikiLink Stationary_process.
- Campbells_theorem_(probability) wikiPageWikiLink Stationary_stochastic_process.
- Campbells_theorem_(probability) wikiPageWikiLink Statistics.
- Campbells_theorem_(probability) wikiPageWikiLink Stochastic_geometry.
- Campbells_theorem_(probability) wikiPageWikiLink Summation.
- Campbells_theorem_(probability) wikiPageWikiLink Vacuum_tube.
- Campbells_theorem_(probability) wikiPageWikiLink Vacuum_tubes.
- Campbells_theorem_(probability) wikiPageWikiLink Variance.
- Campbells_theorem_(probability) wikiPageWikiLinkText "Campbell's theorem (probability)".
- Campbells_theorem_(probability) wikiPageWikiLinkText "Campbell's theorem".
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- Campbells_theorem_(probability) subject Category:Probability_theorems.
- Campbells_theorem_(probability) comment "In probability theory and statistics, Campell's theorem or the Campbell-Hardy theorem can refer to a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the intensity measure of the point process, which allows for the calculation of expected value and variance of the random sum.".
- Campbells_theorem_(probability) label "Campbell's theorem (probability)".
- Campbells_theorem_(probability) sameAs m.0j42yh6.
- Campbells_theorem_(probability) sameAs Q5027968.
- Campbells_theorem_(probability) sameAs Q5027968.
- Campbells_theorem_(probability) wasDerivedFrom Campbells_theorem_(probability)oldid=679313719.
- Campbells_theorem_(probability) isPrimaryTopicOf Campbells_theorem_(probability).