The best replacement for continuous variables is discrete variables.

The best alternatives to continuous variables are rated as following:
★★★★★  discrete variables
★★  random variables
★  categorical variables

Your alternative for continuous variables is not listed? Suggest!
Speaking about continuous variables, one probably shouldn't forget about logistic regression.

Other search terms related to continuous variables and their ratings are:
★★★★★ logistic regression
You have in mind a companion for continuous variables and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of continuous variables in all years. Click on graph for more.
continuous variables
discrete variables
random variables