Another suggestion from machine learning stuff to throw into the mix: A soft step function that we use often is y = e^(ax) / ( 1 + e^(ax)). It has the nice property that the result y is always in (0,1). If you invert this, you get x = -(1/a)*log(y - 1); this maps (0,1) to the whole real line, and the a parameter controls how sharp that mapping is. Now use that as the input to a Gaussian, and you can get a soft truncation at (0,1).
Additionally, you can do this twice to have more control over the shape of the resulting distribution. I suspect the resulting kurtosis/skew factors would be calculable. This has the advantage of giving you a calculable pdf (just normalize the resulting distribution using the inverse det-of-Jacobian factor) without too much hassle. Furthermore, it should be easy to fit the parameters to data without too much difficulty (though I haven't tried). Just a thought, though I've never worked with all this much so I can't say for sure how well it would work. --Hoyt On Fri, Apr 25, 2008 at 4:39 PM, Charles R Harris <[EMAIL PROTECTED]> wrote: > > > > On Fri, Apr 25, 2008 at 1:25 PM, Rich Shepard <[EMAIL PROTECTED]> > wrote: > > > > On Fri, 25 Apr 2008, Charles R Harris wrote: > > > > > You can use something like f(x) = (1-x**2)**2 , which has inflection > > > points and vanishes at +/- 1. Any of the B-splines will also do the > trick. > > > > Chuck, > > > > Thank you. I need to make some time to understand the B-splines to use > > them appropriately. Unfortunately, my mathematical statistics learning was > > many years in the past ... but we had moved ahead of writing on clay > tablets > > by that time. Not needing to retain that knowledge for many years means it > > was replaced by more pressing current knowledge. The B-splines do look > > promising, though. > > > > > > > > > > Here's a B-spline approximation to a Gaussian: > http://www.doc.ic.ac.uk/~dfg/AndysSplineTutorial/BSplines.html > > Chuck > > > > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://projects.scipy.org/mailman/listinfo/numpy-discussion > > -- +++++++++++++++++++++++++++++++++++ Hoyt Koepke UBC Department of Computer Science http://www.cs.ubc.ca/~hoytak/ [EMAIL PROTECTED] +++++++++++++++++++++++++++++++++++ _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
