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%%\hfill{Final English version edited by ES 30.4.99}\\
\noindent{\bf Vilfredo Federigo Samaso PARETO}\\
b. 15 July 1848 - d. 19 August 1923
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\noindent
{\bf Summary} Pareto showed empirically in 1896 that the distribution of income
was asymptotically $x^{-\alpha}$, thus discovering the very first case of a
stable non-Gaussian probability distribution.
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Vilfredo Pareto was born in Paris, where his father, the Marquis Raffaele
Pareto (1812-1882), an engineer from an old Genoese family, was in
exile at the time for political reasons.  His mother, Marie
M\'etenier (1816-1889), was French, so that French was Pareto's
mother tongue; it was only after the family's return to the
Piedmont in 1852 that he mastered Italian. He had two sisters who left no
progeny.

His first wife whom he married in 1889 was a Russian aristocrat,
Alexandrina (Dina) Bakounine, who left him in 1900.  He remarried
to Jeanne Regis, a Frenchwoman with whom he had been living for
twenty years, two months before his death.
As he had no children,
he left his fairly considerable fortune to her, having earlier
donated his
library to the University of Lausanne in 1908.
He is buried at C\'eligny near Geneva in Switzerland, where
he had been residing since 1900.

His life, public, intellectual and professional is fairly neatly
divided into three phases.

\noindent {\bf 1.} The period from his birth till 1870 was the
 formative phase. This was basically scientific and technical,
although Pareto learned Greek and Latin by himself and became a
discriminating connoisseur of these languages.  He first attended
the Leardi Technical Institute
at Casale Monferrato (Piedmont) from 1859-1861, then the
Royal Technical Institute of Turin (1861-1864). This was followed by
the University of Turin (Torino), where he obtained his degree in the
Mathematical and Physical Sciences in 1867, and finally by the School
of Applied Engineering of this University. He was awarded his
engineering diploma following a thesis on {\it La th\'eorie de l'\'elasticit\'e
des corps solides et l'int\'egration des e\'quations differentielles qui
d\'efinissent l'\'equilibre.}

\noindent {\bf 2.} From 1870 to 1873, Pareto worked as an engineer on the
Italian railways, then in 1873 joined a firm building railway material
at San Giovanni Valdarno in Tuscany.  He managed this firm from
1880 to 1890, becoming a consultant between 1890 and 1893.  It
was during this period, when he faced the economic and
social problems of
managing the firm that he became vitally
interested in economics and sociology.

In 1874 he took part in the creation of the Soci\'et\'e Adam Smith
. During this  period he wrote several papers for
{\it L'economista} from 1876, the {\it Journal des Economistes} from
1887 and for the {\it Monde \'economique} and the {\it Giornale degli
Economisti}. He also presented several communications at conferences.

He was resolutely in favour of a liberal economy, but he was also a
pacifist and an anti-colonialist.  He stood for election to the
Chamber of Deputies but was not successful.

He travelled extensively abroad, residing on
occasion in France, Germany, Austria, England, Belgium and
Switzerland.  In 1891 in Switzerland  he met L\'eon Walras, whom
he was to succeed in 1893 in the Chair of Political Economy at the
University of Lausanne.

\noindent {\bf 3.} From 1893 on, he devoted himself to teaching and research.
As an economist he was a follower of A. Cournot (q.v.) and L. Walras in
mathematical economics. His main innovation was a definition of
equilibrium (Pareto's optimum) which is still in use today.  But
Pareto valued theory only insofar as it stood the test of reality;
it was one of the reasons for his interest in statistics and for his
work in this field.

As a sociologist, he was convinced that economic facts were
inseparable from the society which engendered them.  Thus, from 1897
until his retirement in 1911, he taught sociology as
well.

It was during this period that his three main books were published:

\noindent
{\it Cours d'\'economie politique}, Lausanne, Vol.1 (1896) and
Vol.2 (1897).

\noindent{\it Manuale di economia politica con una introduzione alla scienza
sociale}, Milano, 1906 (French translation: {\it Manuel d'Economie
politique}, Paris, 1909).

\noindent{\it Trattato di Sociologia}, Firenze, 1916 (French edition:
{\it Trait\'e de Sociologie}, Lausanne, 1917).

In {\it statistics}  Pareto worked in three areas:


\noindent{\bf (a)} Interpolation and fitting methods to which he devoted several
papers, in particular those in the {\it Journal de la Soci\'et\'e
Statistique de Paris}, November 1897, and in the {\it Zeitschrift
f\"ur schweizerische Statistik}, XXXV, 1899, as well as the {\it
Actes du IV\`eme Congr\`es International de Psychologie}
(Geneva, 1909).
\smallskip

\noindent{\bf (b)} Actuarial studies on mutual insurance systems and the
calculation of pensions. He worked on these in 1905 in response to
a request from the employees of the Swiss Federal Railways.
\smallskip

The main works which he published in the two areas (a) and (b) have
been republished in Pareto (1989), where his
paper  ``Sur les fonctions g\'en\'eratrices d'Abel" in pure
mathematics, published in Kronecker's {\it Journal f\"ur die reine und
angewandte Mathematik }, {\bf 110} (1892), 290-323, is also to be found.
\smallskip

\noindent{\bf (c)} But it was mainly his discovery in 1895 of the
 ``Distribution curve for wealth and incomes" that Pareto is
renowned as a statistician.
He showed empirically that the
observed distribution of incomes, like that of wealth was
well fitted by theoretical distributions of the type

\begin{equation}
Pr(X > x) = \frac {K}{(x + c)^\alpha},
x \geq x_0,
\end{equation}
$K$ and $c$ being respectively parameters of scale
and location while the exponent $\alpha$, for the series studied
by Pareto, takes values between 1 and 2 (see Pareto, 1964, 1965).

Later, this kind of distribution was found to arise in various 
fields, not only in the social sciences, but also in the natural
and  physical sciences.  Various probabilistic models lead to such
distributions: Pareto himself had attempted to develop probabilistic models
as early as 1896 (see Pareto, 1964, supplements to Vol.2, pp.416-419).
Thirty years later Maurice Fr\'echet (q.v.) was to perfect Pareto's model.

The most profound reason for the frequency with which Pareto
distributions appear was given in 1935 by Paul L\'evy (1937), namely
that stable
distributions, other than the Laplace-Gauss ( Normal) distribution, exhibit 
the asymptotic  behaviour of 
type (1), with $0 < \alpha < 2$.

Further, when conditions for convergence to the
Normal distribution in the Central Limit Theorem do not apply, namely 
when dealing with independent identically-distributed random summands 
whose large values have a non-negligible
probability (heavy tailed distributions), if these distributions have 
tail behaviour asymptotically of  type (1), then a Central Limit Theorem
result still holds, with stable law of exponent $\alpha$ figuring 
as the limit law,
rather than the Normal.

It is thus to Pareto that belongs the immense credit
for breaking the almost total monopoly of the
Gaussian (Normal) distribution and its domain of attraction in statistics.
Unfortunately it only earned him the lack of understanding and
hostility of his peers, in particular F.Y. Edgeworth (q.v.).
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\begin{thebibliography}{3}
\bibitem{1}  Pareto, V. (1964). {\it Cours d'\'Economie Politique}, Droz, Geneva.
[This is a new edition by G.H. Bousquet and G. Busino.]

\bibitem{2}  Pareto, V. (1965). {\it \'Ecrits sur la courbe de r\'epartition de
la richesse}.  Droz, Geneva. [Collected with commentary by  G. Busino.]
 
\bibitem{3} Pareto, V. (1989). {\it Statistique et \'Economie math\'ematique}.
Droz, Geneva. [Preface by Ren\'e Roy.] 

\bibitem{4}  L\'evy, P. (1937). {\it Th\'eorie de l'addition des variables
 al\'eatoires}.  Gauthier-Villars,  Paris.
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\hfill{Marc Barbut}



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