@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:-HXQXV6V2-F
  skos:prefLabel "logit function"@en, "fonction logit"@fr ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Logit>, <https://fr.wikipedia.org/wiki/Logit> ;
  skos:definition """In statistics, the <b>logit</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'l' in 'lie'">l</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="/dʒ/: 'j' in 'jam'">dʒ</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span><span title="'t' in 'tie'">t</span></span>/</span></span> <i title="English pronunciation respelling"><span style="font-size:90%">LOH</span>-jit</i>) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations.
<br/>Mathematically, the logit is the inverse of the standard logistic function <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 (x)=1/(1+e^{-x})}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>σ<!-- σ --></mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mn>1</mn>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mo>/</mo>
<br/>        </mrow>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mn>1</mn>
<br/>        <mo>+</mo>
<br/>        <msup>
<br/>          <mi>e</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>x</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sigma (x)=1/(1+e^{-x})}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d652eb008d808b8f71210bb3d2fe48a5ee451a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:19.239ex; height:3.009ex;" alt="\\\\sigma (x)=1/(1+e^{-x})"></span>, so the logit is defined as
<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 \\\\operatorname {logit} p=\\\\sigma ^{-1}(p)=\\\\ln {\\rac {p}{1-p}}\\\\quad {\\	ext{for}}\\\\quad p\\\\in (0,1).}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>logit</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mi>p</mi>
<br/>        <mo>=</mo>
<br/>        <msup>
<br/>          <mi>σ<!-- σ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>p</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mi>ln</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mi>p</mi>
<br/>            <mrow>
<br/>              <mn>1</mn>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mi>p</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtext>for</mtext>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mi>p</mi>
<br/>        <mo>∈<!-- ∈ --></mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mn>0</mn>
<br/>        <mo>,</mo>
<br/>        <mn>1</mn>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\operatorname {logit} p=\\\\sigma ^{-1}(p)=\\\\ln {\\rac {p}{1-p}}\\\\quad {\\	ext{for}}\\\\quad p\\\\in (0,1).}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d6547728512aea39afff31b71329766070e240c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:44.51ex; height:5.343ex;" alt="{\\\\displaystyle \\\\operatorname {logit} p=\\\\sigma ^{-1}(p)=\\\\ln {\\rac {p}{1-p}}\\\\quad {\\	ext{for}}\\\\quad p\\\\in (0,1).}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Logit">https://en.wikipedia.org/wiki/Logit</a>)"""@en, """La <b>fonction logit</b> est une fonction mathématique utilisée principalement
<br/>
<br/><ul><li>en statistiques et pour la régression logistique,</li>
<br/><li>en intelligence artificielle (réseaux neuronaux),</li>
<br/><li>en inférence bayésienne pour transformer les probabilités sur [0,1] en <i>évidence</i> sur ℝ afin d'une part d'éviter des renormalisations permanentes, et d'autre part de rendre additive la formule de Bayes pour faciliter les calculs.</li></ul>
<br/>Son expression est 
<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 \\\\operatorname {logit} (p)=\\\\ln \\\\left({\\rac {p}{1-p}}\\
ight)\\\\!\\\\,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>logit</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>p</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mi>ln</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mfrac>
<br/>              <mi>p</mi>
<br/>              <mrow>
<br/>                <mn>1</mn>
<br/>                <mo>−<!-- − --></mo>
<br/>                <mi>p</mi>
<br/>              </mrow>
<br/>            </mfrac>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\operatorname {logit} (p)=\\\\ln \\\\left({\\rac {p}{1-p}}\\
ight)\\\\!\\\\,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e39afd1bfd14e1ae7dae421410e267de19b16f91" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:21.969ex; height:6.176ex;" alt="{\\\\displaystyle \\\\operatorname {logit} (p)=\\\\ln \\\\left({\\rac {p}{1-p}}\\
ight)\\\\!\\\\,}"></span> où <i>p</i> est défini sur ]0, 1[</dd> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Logit">https://fr.wikipedia.org/wiki/Logit</a>)"""@fr ;
  skos:broader psr:-FH1H1FB9-1 ;
  dc:created "2023-07-28"^^xsd:date ;
  dc:modified "2023-07-28"^^xsd:date ;
  a skos:Concept .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-HXQXV6V2-F .