skew me with your flexible parameter
August 28, 2006 7:14 AM Subscribe
FunctionFilter: I need a function that allows me to skew a distribution from a uniform distribution to an extremely biased distribution for a domain and range of (0,1).
posted by allan to Science & Nature (6 answers total)
I think I'm looking for a CDF, but I can work with the details. The problem is that both the domain and range have to be between 0 and 1. This rules out a natural choice of a simple exponential. The inverse CDF should have a single inflection point which will always be on the line y=x. I would like to be able to tune the function with a single parameter between a uniform distribution (CDF: y=-1+1) and something like an exponential function y=n* e^(-nx) except with the asymptotes approaching the axes at 0 and 1.
In other words, f(0) approaches 1 and f(1) approaches 0. I need a function that allows me to tune how steeply they approach, and the function must be symetric around y=x. I feel like such a function must exist, but I can't find it in any of the standard stats references. It's for a simulation, so I can fudge behavior at 0 and 1 if needs be. Any ideas?