Cloglog Link Function

Cloglog link models extreme events effectively, transforming target values using Gumbel distribution.

The Complimentary Log-Log (cloglog) link is another example of using an inverse cumulative distribution function to transform the target. It differs from logit and probit function because it is asymmetric. It works best when the chance of an event is extremely low or extremely high. Gumbel described these extreme value distributions. The cloglog model is closely related to continuous-time models for event occurrence. The cloglog link function corresponds to Gumbel CDF. The precipitation from the worst rainstorm in 100 years is an example of data that follows an extreme value distribution (the hundred year rain).