Statistical results of continuous, finite, closed form functions


New Member
I've done a lot of digging but all the keywords point to continuous random variables, and that's not what I'm interested in. I'm interested in the statistics of a known, closed form, continuous algebraic expression, f(t) over some domain off t. The simplest computational approach is to create a large array of discrete samples with some uniform spacing deltat, based on smoothness, and then apply the calculations used for sampled random variable data. What I'm interested in is if there are analytic techniques that avoid artificially sampling the continuous function into large arrays. Right now I's be satisfied with information pertaining to continuous real valued functions, although complex valued functions of a single real variable are of interest. Simple results such as PDF, CDF, CCDF, etc. are desired. I suspect that this is not a typical question in a statistics forum where random variable analysis is the entirety of the subject matter, but where else ccould I ask this odd question. Thanks for any feedback!!!