please. if possible, give some justifications on why it is common and what factors influence their suitability
Probability distribution method? Read the work of Peter ED Love and David Baccarini
Probability is a good alternative to start if you don't have experience data. If you have experience data on previous projects then you have a starting point to see what are the most important factors driving the (consumed) contingencies and the amount of contingency you need. From there you can use analogy comparisons to verify whether the factors apply to your project.
Cost contingency and cost estimate process in general are based upon experience and historical information. The process can not be done without any of those two pillars. If you do not have information, you do not have probability distribution or any other thing. Probability is the best when you have tons of data.
Contingency should be the probable cost of the unknowns at the time of the estimate. Current computing power has reached a point where it is possible to develop data-driven cost models in MS Excel where the use of Monte Carlo simulations permit a rational contingency to be developed based on a desired level of confidence.
You will find good papers on the topic at www.aacei.org.