The logit transformation applies the logit function 
to map a probability 
to its log-odds. In logistic
regression, the log-odds of the conditional
probability of success are a linear function
of the explanatory variables. For two probabilities 
and 
in 
, the difference of the transformed
values is the natural logarithm of the odds
ratio,
 |
(1)
|
The transformation has an inflection point at 
, where its second derivative
 |
(2)
|
changes sign.
The transformation has also been used to generate random numbers from the logistic map 
(Collins et al. 1992). If the initial
value is drawn from a stationary distribution
of the map with probability density function 
for 
, each transformed value 
has probability
density function
 |
(3)
|
for 
. Collins et al. (1992) describe this density
as close to that of a normal distribution.
Successive values are dependent because each value determines the next.
