# [pstricks] Drawing S- and Z-Curves

Michael Sharpe msharpe at ucsd.edu
Wed Apr 22 01:38:20 CEST 2009

```Rich,

For the bell shaped curve with value 1 at x=m, variance v, plotted
from x=a to x=b, you could use

\psplot[algebraic]{a}{b}{Ex(-(x-m)^2/v)}

where, of course, specific numbers should be substituted for m, v, a, b.

A similar expression can be constructed for the particular logistic
curve (S-curve) you need, possibly expressed most simply using \tanh,
written th in algebraic formulas. Eg

\psplot[algebraic]{a}{b}{(1+th(x/2))/2}

Michael

On Apr 21, 2009, at 3:45 PM, Rich Shepard wrote:

> On Tue, 21 Apr 2009, Michael Sharpe wrote:
>
>> Both S-curves and Z-curves, as I know them, are defined by
>> functions known
>> to Postscript, so there is no need for Bezier approximations.
>
> Michael,
>
>   Oh. Guess I need to go find those. I vaguely recall it takes extra
> code to
> place raw PS in the PSTricks .tex file. Is that correct?
>
>> Of course, both those terms have multiple meanings, but I assume that
>> Z-curve means a normal density curve (two parameters) and S-curve
>> means a
>> logistic curve (3 parameters.)
>
>   In the realm of approximate reasoning models, a Z-curve is 1-S-
> curve. In
> the .eps example I attached to my initial post, the left-most curve
> is a
> Z-curve, the middle ones are normal/bell/Gaussian curves, and the
> right-most
> is an S-curve. A Z-curve starts at y=1.0 and ends at y=0.0; an S-
> curve is
> the opposite.
>
>   Yes, different disciplines assign different meaning to the same
> term.
>
> Rich
>
> --
> Richard B. Shepard, Ph.D.               |  Integrity
> Credibility
> Applied Ecosystem Services, Inc.        |            Innovation
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```