Hi.
I'm trying to derive the variance (or stddev) of the logistic
distribution, as follows.
(%i1) cdf:1/(1+exp(-x/s));
1
(%o1) -----------
- x/s
%e + 1
(%i2) pdf:diff(cdf,x);
- x/s
%e
(%o2) ----------------
- x/s 2
s (%e + 1)
(%i3) var:integrate(pdf*x^2,x,-inf,inf);
Is s positive or negative?
pos;
1
Is - an integer?
s
no;
2
Is - an integer?
s
no;
Integral is divergent
-- an error. Quitting. To debug this try debugmode(true);
(%i4)
Now wikipedia claims %pi^2 * s^2 / 3 is the correct variance. Which
means that this integral should not be divergent unless I'm missing
something. What is going on?
When I say yes to the 1/s or 2/s queries, I get a result, but it's not
the one that wikipedia claims.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan