@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:-HMVJL63M-G
  skos:prefLabel "Gaussian integral"@en, "intégrale de Gauss"@fr ;
  a skos:Concept ;
  skos:related psr:-XQF2FLQF-B .

psr: a skos:ConceptScheme .
psr:-XQF2FLQF-B
  skos:altLabel "Gaussian distribution"@en, "loi de Laplace-Gauss"@fr, "loi gaussienne"@fr, "loi de Gauss"@fr ;
  skos:broader psr:-K9FXDR6F-N, psr:-FH1H1FB9-1 ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Normal_distribution>, <https://fr.wikipedia.org/wiki/Loi_normale> ;
  skos:inScheme psr: ;
  skos:definition """En théorie des probabilités et en statistique, les lois normales sont parmi les lois de probabilité les plus utilisées pour modéliser des phénomènes naturels issus de plusieurs événements aléatoires. Elles sont en lien avec de nombreux objets mathématiques dont le mouvement brownien, le bruit blanc gaussien ou d'autres lois de probabilité. Elles sont également appelées lois gaussiennes, lois de Gauss ou lois de Laplace-Gauss des noms de Laplace (1749-1827) et Gauss (1777-1855), deux mathématiciens, astronomes et physiciens qui l'ont étudiée. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Loi_normale">https://fr.wikipedia.org/wiki/Loi_normale</a>)"""@fr, """In statistics, a <b>normal distribution</b> or <b>Gaussian distribution</b> is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
<br/>
<br/><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)={\\rac {1}{\\\\sigma {\\\\sqrt {2\\\\pi }}}}e^{-{\\rac {1}{2}}\\\\left({\\rac {x-\\\\mu }{\\\\sigma }}\\
ight)^{2}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mrow>
<br/>              <mi>σ<!-- σ --></mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <msqrt>
<br/>                  <mn>2</mn>
<br/>                  <mi>π<!-- π --></mi>
<br/>                </msqrt>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <msup>
<br/>          <mi>e</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mn>2</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <msup>
<br/>              <mrow>
<br/>                <mo>(</mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mfrac>
<br/>                    <mrow>
<br/>                      <mi>x</mi>
<br/>                      <mo>−<!-- − --></mo>
<br/>                      <mi>μ<!-- μ --></mi>
<br/>                    </mrow>
<br/>                    <mi>σ<!-- σ --></mi>
<br/>                  </mfrac>
<br/>                </mrow>
<br/>                <mo>)</mo>
<br/>              </mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msup>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f(x)={\\rac {1}{\\\\sigma {\\\\sqrt {2\\\\pi }}}}e^{-{\\rac {1}{2}}\\\\left({\\rac {x-\\\\mu }{\\\\sigma }}\\
ight)^{2}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00cb9b2c9b866378626bcfa45c86a6de2f2b2e40" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.838ex; width:24.446ex; height:6.676ex;" alt="{\\\\displaystyle f(x)={\\rac {1}{\\\\sigma {\\\\sqrt {2\\\\pi }}}}e^{-{\\rac {1}{2}}\\\\left({\\rac {x-\\\\mu }{\\\\sigma }}\\
ight)^{2}}}"></span></dd></dl>
<br/>The parameter <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 \\\\mu }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>μ<!-- μ --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mu }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="\\\\mu "></span> is the mean or expectation of the distribution (and also its median and mode), while the parameter <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 \\\\sigma }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>σ<!-- σ --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sigma }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="\\\\sigma "></span> is its standard deviation. The variance of the distribution is <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 \\\\sigma ^{2}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>σ<!-- σ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sigma ^{2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a5c55e536acf250c1d3e0f754be5692b843ef5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.385ex; height:2.676ex;" alt="\\\\sigma ^{2}"></span>. A random variable with a Gaussian distribution is said to be <b>normally distributed</b>, and is called a <b>normal deviate</b>.
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Normal_distribution">https://en.wikipedia.org/wiki/Normal_distribution</a>)"""@en ;
  skos:related psr:-HMVJL63M-G ;
  skos:prefLabel "loi normale"@fr, "normal distribution"@en ;
  a skos:Concept ;
  dc:modified "2023-08-16"^^xsd:date .

psr:-K9FXDR6F-N
  skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ;
  a skos:Concept ;
  skos:narrower psr:-XQF2FLQF-B .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-XQF2FLQF-B .