Repeated convolution of a continous uniform distribution

My program pw.mac can do this problem symbolically.

first get pw.mac from my site.

http://mysite.verizon.net/res11w2yb/id2.html

then try

 (showtime:true);
Evaluation took 0.0000 seconds (0.0000 elapsed)
(out7) true
convolution(f, g, x) := block([s,p], f:subst(x = p, f), g:subst(x = x - p, g), pwdefint(f * g, p, minf, inf))$
Evaluation took 0.0000 seconds (0.0000 elapsed)
define(boxcar(x), unit_step(x+a)-unit_step(x-a));
Evaluation took 0.0000 seconds (0.0000 elapsed)
(out9) boxcar(x):=unit_step(x+a)-unit_step(x-a)
f1:convolution(boxcar(x),boxcar(x),x);
Evaluation took 0.0800 seconds (0.0800 elapsed)
(out10) ((x+2*a)*signum(x+2*a)+(x-2*a)*signum(x-2*a)-2*x*signum(x))/2
f2:convolution(f1,f1,x)$
Evaluation took 0.2000 seconds (0.2000 elapsed)
f3:convolution(f2,f2,x)$
Evaluation took 4.0400 seconds (4.0400 elapsed)
f4:convolution(f3,f3,x)$
Evaluation took 477.4300 seconds (477.4300 elapsed)
draw2d(
color=black,
explicit(f1,x,-5,5),
color=blue,
explicit(f2,x,-5,5),
color=dark-green,
explicit(f3,x,-5,5),
color=red,
explicit(f4,x,-5,5)),a=1/2$
(%t14)  << Graphics >>
Evaluation took 12.9700 seconds (12.9700 elapsed)


Richard


----- Original Message ----- 
From: <weaker at directbox.com>
To: <maxima at math.utexas.edu>
Sent: Thursday, June 18, 2009 7:30 AM
Subject: Repeated convolution of a continous uniform distribution


Hi  all,

I want to do a repeated convolution of a continous uniform distribution in a limited interval [-a,a].

It is clear to me that after the first convolution there will be a triangular distribution and that it will become broader and 
smoother every time and asymptotically gaussian.

How can I calculate/plot the resulting distribution after x iterations with Maxima?

Best regards,
weaker


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