The Generation of the Fat Tails
distributions
RICCARDO LUCCIO
Dipartimento di Psicologia “G. Kanizsa”, Università di Trieste
8th Alps-Adria Psychology Conference - October 3, 2008
Ljubljana
Benford’s law (Newcomb, 1881)
1

p d   log10  1   .
d

Pareto’s Law
p x  
kx mk
x
k 1
,
Lorenz’ Law
p x  
a
xb

 1
 c 
2
,
Zipf’ law
a
f (r)  k ,
br
Heap’s law
v  an ,
b
Other heavy tail distributions
Bradford’s law;
Lotka’s law;
Towns/inhabitants;
Gerbino’s law;
Firms/workers;
Web accesses;
Drugs/pharmaceutical groups
It follows the Zipf’ law:
QuickTime™ e un
decompressore TIFF (N on compresso)
sono necessari per visualizzare quest'immagine.
Schultz
It follows the Zipf’ law:
QuickTime™ e un
decompressore TIFF (Non compresso)
sono necessari per visualizzare quest'immagine.
Alliterations
All follow Lorenz’law:
p x  
a
xb

 1
 c 
2
,
“Il Piacere” by D’Annunzio
a=-2.832
b=7.524
c=927.990
d=1.327
R2=0.979
“Il Bacio” by Invernizio
a=-.430
b=12.612
c=147.654
d=-1.755
R2=0.989
“Discorso” by Leopardi
a=2.529
b=9.806
c=174.441
d=-1.176
R2=0.976