Skellam distribution (original) (raw)
In teoria delle probabilità la distribuzione di Skellam è una distribuzione di probabilità che governa la differenza tra due variabili aleatorie indipendenti aventi entrambe una distribuzione di Poisson. Prende il nome da John Gordon Skellam.
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| dbo:abstract | En théorie des probabilités et en statistique, la loi de Skellam est la loi de probabilité discrète de la différence de deux variables aléatoires indépendantes N1 et N2 de loi de Poisson de paramètres respectifs μ1 et μ2. Cette loi est utilisée pour décrire la différence entre deux images d'un bruit quantique ou pour comparer les résultats sportifs lors d'égalité des points dans certains sports tels que le baseball, le hockey sur glace et le football. La fonction de masse de la loi de Skellam issue de deux lois de Poisson de paramètres μ1 et μ2 est donnée par : où Ik est la fonction de Bessel modifiée de première espèce. Le nom de cette loi est issue du statisticien et biologiste . (fr) The Skellam distribution is the discrete probability distribution of the difference of two statistically independent random variables and each Poisson-distributed with respective expected values and . It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer. The distribution is also applicable to a special case of the difference of dependent Poisson random variables, but just the obvious case where the two variables have a common additive random contribution which is cancelled by the differencing: see Karlis & Ntzoufras (2003) for details and an application. The probability mass function for the Skellam distribution for a difference between two independent Poisson-distributed random variables with means and is given by: where Ik(z) is the modified Bessel function of the first kind. Since k is an integer we have that Ik(z)=I|k |
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| dbo:wikiPageExternalLink | http://stat-athens.aueb.gr/~jbn/papers/paper11.htm http://store.doverpublications.com/0486612724.html%7Cedition=Unabridged |
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| dbp:median | N/A (en) |
| dbp:name | Skellam (en) |
| dbp:pdfImage | 325 (xsd:integer) (Examples of the probability mass function for the Skellam distribution. The horizontal axis is the index k. ) (en) |
| dbp:type | mass (en) |
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| rdfs:comment | In teoria delle probabilità la distribuzione di Skellam è una distribuzione di probabilità che governa la differenza tra due variabili aleatorie indipendenti aventi entrambe una distribuzione di Poisson. Prende il nome da John Gordon Skellam. (it) The Skellam distribution is the discrete probability distribution of the difference of two statistically independent random variables and each Poisson-distributed with respective expected values and . It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer. where Ik(z) is the modified Bessel function of the first kind. Since k is an integer we have that Ik(z)=I|k |
| rdfs:label | Loi de Skellam (fr) Distribuzione di Skellam (it) Skellam distribution (en) Rozkład Skellama (pl) Распределение Скеллама (ru) |
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