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Inverse logistic function

820 bytes added, 15:56, 31 May 2014
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<math>x \mapsto \ln \left(\frac{x}{1 - x}\right)</math>
 
The function may be extended to a function <math>[0,1] \to [-\infty,\infty]</math> with the value at 0 defined as <math>-\infty</math> and the value at 1 defined as <math>\infty</math>.
 
===Probabilistic interpretation====
 
Given a probability <math>p</math> (strictly between 0 and 1) the inverse logistic function computes the logarithm of the corresponding odds. Explicitly, the odds corresponding to probability <math>p</math> are:
 
<math>\frac{p}{1 - p}</math>
 
The logarithm of the odds is therefore:
 
<math>\ln \left(\frac{p}{1 - p}\right)</math>
 
==Key data==
 
{| class="sortable" border="1"
! Item !! Value
|-
| default [[domain]] || [[open interval]] <math>(0,1)</math>
|-
| [[range]] || all of <math>\R</math>
|-
| [[inverse function]] || [[logistic function]] <math>x \mapsto \frac{1}{1 + e^{-x}}</math>
|}
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