Hello,

Say I have a set of real numbers in a range such as 0 to 1. I am looking for a function that will decrease the value of numbers toward the lower end, increase the value of numbers near the upper end, and leave values in the middle more or less unchanged. The method would need to work on any range of numbers, but I use 0 to 1 as an example.

I have looked at something in the form of,

Modifying a and b will alter the upper and lower ends of a range of numbers, but after playing around a bit I can't seem to get both ends in line at the same time. I don't know if I need one more term of if I am thinking about this in the wrong way so I though I would post. I was originally thinking of a sigmoid, but that doesn't give anything like the results I am looking for.

I can post data if that would help, just let me know.

Anything ring a bell?

Thanks,

LMHmedchem