@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:-K9FXDR6F-N
  skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ;
  a skos:Concept ;
  skos:narrower psr:-HQ8K4278-V .

psr:-HQ8K4278-V
  skos:broader psr:-K9FXDR6F-N ;
  skos:exactMatch <https://en.wikipedia.org/wiki/U-quadratic_distribution>, <https://fr.wikipedia.org/wiki/Loi_parabolique> ;
  skos:inScheme psr: ;
  skos:prefLabel "loi parabolique"@fr, "U-quadratic distribution"@en ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """In probability theory and statistics, the <b>U-quadratic distribution</b> is a continuous probability distribution defined by a unique convex quadratic function with lower limit <i>a</i> and upper limit <i>b</i>.  <dl><dd><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 f(x|a,b,\\\\alpha ,\\eta )=\\\\alpha \\\\left(x-\\eta \\
ight)^{2},\\\\quad {\\	ext{for }}x\\\\in [a,b].}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>f</mi>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mrow class="MJX-TeXAtom-ORD">           <mo stretchy="false">|</mo>         </mrow>         <mi>a</mi>         <mo>,</mo>         <mi>b</mi>         <mo>,</mo>         <mi>α<!-- α --></mi>         <mo>,</mo>         <mi>β<!-- β --></mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mi>α<!-- α --></mi>         <msup>           <mrow>             <mo>(</mo>             <mrow>               <mi>x</mi>               <mo>−<!-- − --></mo>               <mi>β<!-- β --></mi>             </mrow>             <mo>)</mo>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>,</mo>         <mspace width="1em"></mspace>         <mrow class="MJX-TeXAtom-ORD">           <mtext>for </mtext>         </mrow>         <mi>x</mi>         <mo>∈<!-- ∈ --></mo>         <mo stretchy="false">[</mo>         <mi>a</mi>         <mo>,</mo>         <mi>b</mi>         <mo stretchy="false">]</mo>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle f(x|a,b,\\\\alpha ,\\eta )=\\\\alpha \\\\left(x-\\eta \\
ight)^{2},\\\\quad {\\	ext{for }}x\\\\in [a,b].}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be007a45776e57f52c0de6df1e6c595860ae7a9a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.26ex; height:3.343ex;" alt="{\\\\displaystyle f(x|a,b,\\\\alpha ,\\eta )=\\\\alpha \\\\left(x-\\eta \\
ight)^{2},\\\\quad {\\	ext{for }}x\\\\in [a,b].}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/U-quadratic_distribution">https://en.wikipedia.org/wiki/U-quadratic_distribution</a>)"""@en, """En théorie des probabilités et en statistique, la <b>loi parabolique</b> est une loi de probabilité continue dont la densité de probabilité est définie à partir d'une fonction polynomiale de degré deux, c'est-à-dire une fonction <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 f(x)=\\\\alpha \\\\left(x-\\eta \\
ight)^{2}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>f</mi>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <mi>α<!-- α --></mi>         <msup>           <mrow>             <mo>(</mo>             <mrow>               <mi>x</mi>               <mo>−<!-- − --></mo>               <mi>β<!-- β --></mi>             </mrow>             <mo>)</mo>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle f(x)=\\\\alpha \\\\left(x-\\eta \\
ight)^{2}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfbc092311232d5abb33790ca5271d6ef61cc904" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.369ex; height:3.343ex;" alt="{\\\\displaystyle f(x)=\\\\alpha \\\\left(x-\\eta \\
ight)^{2}}"></span> qui dépend de deux paramètres. Cette loi est également appelée <b>loi parabolique de forme <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 \\\\cup }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo>∪<!-- ∪ --></mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\cup }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8ff7d0293ad19b43524a133ae5129f3d71f2040" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\\\\displaystyle \\\\cup }"></span></b>. De manière similaire on peut définir la <b>loi parabolique de forme <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 \\\\cap }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo>∩<!-- ∩ --></mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\cap }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\\\\displaystyle \\\\cap }"></span></b>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Loi_parabolique">https://fr.wikipedia.org/wiki/Loi_parabolique</a>)"""@fr ;
  dc:created "2023-07-28"^^xsd:date ;
  skos:altLabel "loi parabolique de forme U"@fr .