Edited: I have been researching about density function estimation from a sample of data, and I noticed that there are a lot of researches the estimate the density with the normalizing factor and others that don't.
What are the real world applications of knowing the normalizing constant of the density?
I noticed that if we just want to rank the data by density we don't really need the factor as it is a constant, except for the mathematical meaning that the integral of the density should equal to 1, what else is good about knowing it?