Cauchit Link Function

Cauchit link uses the Cauchy distribution to transform target values, suitable for data with infinite variance.

The Cauchit link is another application of an inverse cumulative distribution function to transform the target. In this case, the distribution is the Cauchy distribution. The Cauchy distribution is symmetric, however, it has infinite variance. An infinite variance means the probability decays slowly as the values become more extreme. Such distributions are called fat-tailed. The Cauchit link is often used where fewer assumptions are justified with respect to the distribution of the target. The Cauchit link is used to measure data in binomial form when the variance is not considered to be finite.