@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-DV3Z3618-C
  skos:broader psr:-K9FXDR6F-N ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Loi_g%C3%A9om%C3%A9trique>, <https://en.wikipedia.org/wiki/Geometric_distribution> ;
  dc:created "2023-07-27"^^xsd:date ;
  skos:prefLabel "geometric distribution"@en, "loi géométrique"@fr ;
  skos:definition """En théorie des probabilités et en statistique, la <b>loi géométrique</b> désigne, selon la convention choisie, l'une des deux lois de probabilité suivantes :  <ul><li>la loi du nombre <span class="texhtml mvar" style="font-style:italic;">X</span> d'épreuves de Bernoulli indépendantes de probabilité de succès <span class="texhtml"><i>p</i> ∈ ]0,1[</span> (ou <span class="texhtml"><i>q</i> = 1 – <i>p</i></span> d'échec) nécessaire pour obtenir le premier succès. <span class="texhtml mvar" style="font-style:italic;">X</span> est la variable aléatoire donnant le rang du premier succès. Le support de la loi est alors {1, 2, 3, ...}.</li> <li>La loi du nombre <i><span class="texhtml mvar" style="font-style:italic;">Y = X</span></i> – 1 d'échecs avant le premier succès. Le support de la loi est alors {0, 1, 2, 3, ...}.</li></ul> On dit que <span class="texhtml mvar" style="font-style:italic;">X</span> suit une <b>loi géométrique de paramètre</b> <i>p</i>. Ces deux lois sont différentes. C'est pourquoi il faut préciser la convention choisie en indiquant le support. Dans la suite, sauf mention contraire, on suppose que les valeurs de <span class="texhtml mvar" style="font-style:italic;">X</span> sont les entiers naturels non nuls 1, 2, 3, ...  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Loi_g%C3%A9om%C3%A9trique">https://fr.wikipedia.org/wiki/Loi_g%C3%A9om%C3%A9trique</a>)"""@fr, """In probability theory and statistics, the <b>geometric distribution</b> is either one of two discrete probability distributions:  <ul><li>The probability distribution of the number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle X}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>X</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle X}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\\\\displaystyle X}"></span> of Bernoulli trials needed to get one success, supported on the set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\{1,2,3,\\\\ldots \\\\}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo fence="false" stretchy="false">{</mo>         <mn>1</mn>         <mo>,</mo>         <mn>2</mn>         <mo>,</mo>         <mn>3</mn>         <mo>,</mo>         <mo>…<!-- … --></mo>         <mo fence="false" stretchy="false">}</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\{1,2,3,\\\\ldots \\\\}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e41b50375891bbd58d9d3a64459abdb629fee50" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.637ex; height:2.843ex;" alt="{\\\\displaystyle \\\\{1,2,3,\\\\ldots \\\\}}"></span>;</li> <li>The probability distribution of the number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle Y=X-1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>Y</mi>         <mo>=</mo>         <mi>X</mi>         <mo>−<!-- − --></mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle Y=X-1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2208aa7baf1d07cdb78070b279a9007712dab3cf" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.855ex; height:2.343ex;" alt="{\\\\displaystyle Y=X-1}"></span> of failures before the first success, supported on the set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\{0,1,2,\\\\ldots \\\\}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo fence="false" stretchy="false">{</mo>         <mn>0</mn>         <mo>,</mo>         <mn>1</mn>         <mo>,</mo>         <mn>2</mn>         <mo>,</mo>         <mo>…<!-- … --></mo>         <mo fence="false" stretchy="false">}</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\{0,1,2,\\\\ldots \\\\}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb18e9a1a9837670a4823e5b3658cd3aa8cc8e88" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.637ex; height:2.843ex;" alt="{\\\\displaystyle \\\\{0,1,2,\\\\ldots \\\\}}"></span>.</li></ul> Which of these is called the geometric distribution is a matter of convention and convenience.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Geometric_distribution">https://en.wikipedia.org/wiki/Geometric_distribution</a>)"""@en ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-K9FXDR6F-N
  skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ;
  a skos:Concept ;
  skos:narrower psr:-DV3Z3618-C .