@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:-K5MB6XJJ-Q
  skos:exactMatch <https://fr.wikipedia.org/wiki/Loi_du_demi-cercle>, <https://en.wikipedia.org/wiki/Wigner_semicircle_distribution> ;
  skos:definition """The <b>Wigner semicircle distribution</b>, named after the physicist Eugene Wigner, is the probability distribution on [−<i>R</i>, <i>R</i>] whose probability density function <i>f</i> is a scaled semicircle (i.e., a semi-ellipse) centered at (0, 0):  <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)={2 \\\\over \\\\pi R^{2}}{\\\\sqrt {R^{2}-x^{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>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>2</mn>             <mrow>               <mi>π<!-- π --></mi>               <msup>                 <mi>R</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msup>             </mrow>           </mfrac>         </mrow>         <mrow class="MJX-TeXAtom-ORD">           <msqrt>             <msup>               <mi>R</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mn>2</mn>               </mrow>             </msup>             <mo>−<!-- − --></mo>             <msup>               <mi>x</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mn>2</mn>               </mrow>             </msup>             <mspace width="thinmathspace"></mspace>           </msqrt>         </mrow>         <mspace width="thinmathspace"></mspace>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle f(x)={2 \\\\over \\\\pi R^{2}}{\\\\sqrt {R^{2}-x^{2}\\\\,}}\\\\,}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79d325a59e2758df47e835b0e9949f973cfe6902" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.643ex; height:5.509ex;" alt="{\\\\displaystyle f(x)={2 \\\\over \\\\pi R^{2}}{\\\\sqrt {R^{2}-x^{2}\\\\,}}\\\\,}"></span></dd></dl> for −<i>R</i> ≤ <i>x</i> ≤ <i>R</i>, and <i>f</i>(<i>x</i>) = 0 if <i>|x|</i> &gt; <i>R</i>. The parameter R is commonly referred to as the "radius" parameter of the distribution. The distribution arises as the limiting distribution of the eigenvalues of many random symmetric matrices, that is, as the dimensions of the random matrix approach infinity. The distribution of the spacing or gaps between eigenvalues is addressed by the similarly named Wigner surmise. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Wigner_semicircle_distribution">https://en.wikipedia.org/wiki/Wigner_semicircle_distribution</a>)"""@en, """En théorie des probabilités et en statistique, la loi du demi-cercle ou loi du demi-cercle de Wigner est une loi de probabilité sur l'intervalle [-R,R] et dont le graphe de la densité de probabilité est un demi-cercle de rayon R, centré en 0 et convenablement renormalisé, ce qui en fait, en fait, une ellipse. En anglais, cette loi est nommée Wigner semicircle distribution, d'après le nom du physicien Eugene Wigner. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Loi_du_demi-cercle">https://fr.wikipedia.org/wiki/Loi_du_demi-cercle</a>)"""@fr ;
  skos:inScheme psr: ;
  skos:prefLabel "Wigner semicircle distribution"@en, "loi du demi-cercle de Wigner"@fr ;
  a skos:Concept ;
  skos:broader psr:-K9FXDR6F-N ;
  dc:modified "2024-10-18"^^xsd:date ;
  dc:created "2023-07-28"^^xsd:date .

psr:-K9FXDR6F-N
  skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ;
  a skos:Concept ;
  skos:narrower psr:-K5MB6XJJ-Q .