# Inverse logistic function

## Definition

The **inverse logistic function** or **log-odds function** is a function from the open interval to all of defined as follows:

The function may be extended to a function with the value at 0 defined as and the value at 1 defined as .

### Probabilistic interpretation

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

The logarithm of the odds is therefore:

## Key data

Item | Value |
---|---|

default domain | open interval |

range | all of |

inverse function | logistic function |