# Changes

## Inverse logistic function

, 15:56, 31 May 2014
no edit summary
$x \mapsto \ln \left(\frac{x}{1 - x}\right)$

The function may be extended to a function $[0,1] \to [-\infty,\infty]$ with the value at 0 defined as $-\infty$ and the value at 1 defined as $\infty$.

===Probabilistic interpretation====

Given a probability $p$ (strictly between 0 and 1) the inverse logistic function computes the logarithm of the corresponding odds. Explicitly, the odds corresponding to probability $p$ are:

$\frac{p}{1 - p}$

The logarithm of the odds is therefore:

$\ln \left(\frac{p}{1 - p}\right)$

==Key data==

{| class="sortable" border="1"
! Item !! Value
|-
| default [[domain]] || [[open interval]] $(0,1)$
|-
| [[range]] || all of $\R$
|-
| [[inverse function]] || [[logistic function]] $x \mapsto \frac{1}{1 + e^{-x}}$
|}
3,138
edits