@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr: a skos:ConceptScheme . psr:-K9FXDR6F-N skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ; a skos:Concept ; skos:narrower psr:-S9QWSS3P-9 . psr:-S9QWSS3P-9 skos:exactMatch , ; skos:definition """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

N 1

N 2

de loi de Poisson de paramètres respectifs

μ 1

μ 2

. 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

μ 1

μ 2

est donnée par :

{\\\\displaystyle f(k;\\\\mu _{1},\\\\mu _{2})=\\\\mathrm {e} ^{-(\\\\mu _{1}+\\\\mu _{2})}\\\\left({\\\\mu _{1} \\\\over \\\\mu _{2}}\\ ight)^{k/2}I_{|k|}(2{\\\\sqrt {\\\\mu _{1}\\\\mu _{2}}})}

où

I k

est la fonction de Bessel modifiée de première espèce. Le nom de cette loi est issue du statisticien et biologiste John Gordon Skellam.
(Wikipedia, L'Encylopédie Libre, https://fr.wikipedia.org/wiki/Loi_de_Skellam)"""@fr, """The Skellam distribution is the discrete probability distribution of the difference

{\\\\displaystyle N_{1}-N_{2}}

of two statistically independent random variables

{\\\\displaystyle N_{1}}

and

{\\\\displaystyle N_{2},}

each Poisson-distributed with respective expected values

{\\\\displaystyle \\\\mu _{1}}

and

{\\\\displaystyle \\\\mu _{2}}

. 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

{\\\\displaystyle K=N_{1}-N_{2}}

between two independent Poisson-distributed random variables with means

{\\\\displaystyle \\\\mu _{1}}

and

{\\\\displaystyle \\\\mu _{2}}

is given by:

{\\\\displaystyle p(k;\\\\mu _{1},\\\\mu _{2})=\\\\Pr\\\\{K=k\\\\}=e^{-(\\\\mu _{1}+\\\\mu _{2})}\\\\left({\\\\mu _{1} \\\\over \\\\mu _{2}}\\ ight)^{k/2}I_{k}(2{\\\\sqrt {\\\\mu _{1}\\\\mu _{2}}})}

where I_k(z) is the modified Bessel function of the first kind. Since k is an integer we have that I_k(z)=I_|k|(z).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Skellam_distribution)"""@en ; skos:broader psr:-K9FXDR6F-N ; skos:inScheme psr: ; dc:modified "2024-10-18"^^xsd:date ; skos:prefLabel "Skellam distribution"@en, "loi de Skellam"@fr ; a skos:Concept ; dc:created "2023-07-27"^^xsd:date .