I use
phi(x):= .5*(1.+erf(a*(x-xb)));
with a and xb as parameters to control the stepnees
also (tanh((x - xb)*a) + 1.) is good
Daniel Lakeland wrote:
> I've been considering a "smooth step" function such as
> 1/(1+exp(-100*x)). I don't anticipate any very quickly growing
> functions which might make the near-but-not-exactly zero portion of
> this function (ie. to the left of x=0) diverge. Since it would be very
> useful to be able to integrate my "spending rates" and determine the
> probability distribution of total project costs at different times in
> the future (based on monte-carlo methods) it would be nice to have a
> smooth step function.
>
> Does anyone have recommendations on a better "smooth step" than the
> one I suggest above? (ie. one that makes for simpler integrals or one
> that is dominant over a larger class of functions without complicating
> the integrals uneccessarily)
>
> Thanks!
> Dan
>
>