Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Campbell's_theorem_(probability)> ?p ?o. }
Showing items 1 to 20 of
20
with 100 items per page.
- Campbell's_theorem_(probability) abstract "In probability theory and statistics, Campell's 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 shot noise, 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.".
- Campbell's_theorem_(probability) wikiPageID "34929672".
- Campbell's_theorem_(probability) wikiPageRevisionID "590793258".
- Campbell's_theorem_(probability) hasPhotoCollection Campbell's_theorem_(probability).
- Campbell's_theorem_(probability) subject Category:Probability_theorems.
- Campbell's_theorem_(probability) type Abstraction100002137.
- Campbell's_theorem_(probability) type Communication100033020.
- Campbell's_theorem_(probability) type Message106598915.
- Campbell's_theorem_(probability) type ProbabilityTheorems.
- Campbell's_theorem_(probability) type Proposition106750804.
- Campbell's_theorem_(probability) type Statement106722453.
- Campbell's_theorem_(probability) type Theorem106752293.
- Campbell's_theorem_(probability) comment "In probability theory and statistics, Campell's 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.".
- Campbell's_theorem_(probability) label "Campbell's theorem (probability)".
- Campbell's_theorem_(probability) sameAs m.0j42yh6.
- Campbell's_theorem_(probability) sameAs Q5027968.
- Campbell's_theorem_(probability) sameAs Q5027968.
- Campbell's_theorem_(probability) sameAs Campbell's_theorem_(probability).
- Campbell's_theorem_(probability) wasDerivedFrom Campbell's_theorem_(probability)?oldid=590793258.
- Campbell's_theorem_(probability) isPrimaryTopicOf Campbell's_theorem_(probability).