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| This article ''Iren&eacute;e-Jules Bienaym&eacute;'' was adapted from an original article by E. Seneta, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/Irenee-JulesBienaymeBienayme.html</nowiki> StatProb Source], Local Files: [[Media:Bienayme.pdf|pdf]] | [[Media:Bienayme.tex|tex]]) is copyrighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the [[:Category:Statprob|Category StatProb]].
+
| This article ''Irenée-Jules Bienaymé'' was adapted from an original article by E. Seneta, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/Irenee-JulesBienaymeBienayme.html</nowiki> StatProb Source], Local Files: [[Media:Bienayme.pdf|pdf]] | [[Media:Bienayme.tex|tex]]) is copyrighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the [[:Category:Statprob|Category StatProb]].
 
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     \begin{document}  
 
     \begin{document}  
 
     \noindent -->
 
     \noindent -->
'''Iren&eacute;e-Jules BIENAYM&Eacute;'''
+
'''Irenée-Jules BIENAYMé'''
  
 
b. 28 August 1796 - d. 19 October 1878
 
b. 28 August 1796 - d. 19 October 1878
  
 
<!-- \noindent -->
 
<!-- \noindent -->
'''Summary.''' Bienaym&eacute; was a Civil Servant. A disciple of Laplace, he
+
'''Summary.''' Bienaymé was a Civil Servant. A disciple of Laplace, he
proved the Bienaym&eacute;-Chebyshev Inequality some years before Chebyshev, and
+
proved the Bienaymé-Chebyshev Inequality some years before Chebyshev, and
 
stated the Criticality Theorem of branching processes completely correctly in
 
stated the Criticality Theorem of branching processes completely correctly in
 
1845. His work on corrrecting the use of the Duvillard life table is perhaps his
 
1845. His work on corrrecting the use of the Duvillard life table is perhaps his
 
greatest achievement as statistician in the public domain.
 
greatest achievement as statistician in the public domain.
  
Bienaym&eacute; was born in Paris but began his secondary education at the ''lyc&eacute;e''
+
Bienaymé was born in Paris but began his secondary education at the ''lycée''
 
in Bruges, then part of the French Empire.  His father held a senior administrative
 
in Bruges, then part of the French Empire.  His father held a senior administrative
position in this town before moving his family back to Paris.  Bienaym&eacute; entered the
+
position in this town before moving his family back to Paris.  Bienaymé entered the
&Eacute;cole Polytechnique in 1815, but this institution was closed in 1816 due to the
+
école Polytechnique in 1815, but this institution was closed in 1816 due to the
 
fall of the Empire and the return of the Bourbons.  With the death of his father in
 
fall of the Empire and the return of the Bourbons.  With the death of his father in
 
1816, he entered the Ministry of Finances and rose to the rank of Inspector General in
 
1816, he entered the Ministry of Finances and rose to the rank of Inspector General in
 
1836.  While carrying out his responsibilities as public servant, he was to become a
 
1836.  While carrying out his responsibilities as public servant, he was to become a
 
self-made scientist, publishing first on demography and actuarial matters, and then on
 
self-made scientist, publishing first on demography and actuarial matters, and then on
mathematical statistics.  He was elected to the Soci&eacute;t&eacute; Philomatique de Paris
+
mathematical statistics.  He was elected to the Société Philomatique de Paris
 
in January, 1838 and was active in its affairs.  His contributions to its meetings were
 
in January, 1838 and was active in its affairs.  His contributions to its meetings were
 
reported in the now-obscure newspaper-journal ''L'Institut, Paris'', being reprinted at
 
reported in the now-obscure newspaper-journal ''L'Institut, Paris'', being reprinted at
the end of the year in the collections ''Proc&egrave;s-Verbaux de la Soci&eacute;t&eacute;
+
the end of the year in the collections ''Procès-Verbaux de la Société
Philomatique de Paris-Extraits''.  Most of his publications in the period 1837 to 1845
+
Philomatique de Paris - Extraits''.  Most of his publications in the period 1837 to 1845
 
appear in this medium, and are characterized, to the frustration of the reader, by lack
 
appear in this medium, and are characterized, to the frustration of the reader, by lack
 
of mathematical proofs for assertions sometimes far ahead of their time.  The most
 
of mathematical proofs for assertions sometimes far ahead of their time.  The most
 
startling of his contributions occurs in this way when he gives, in 1845, a completely
 
startling of his contributions occurs in this way when he gives, in 1845, a completely
 
correct statement of the Criticality Theorem for simple branching processes, which
 
correct statement of the Criticality Theorem for simple branching processes, which
precedes the partly correct one of F. Galton (q.v.) and H.W. Watson by over 30 years and the
+
precedes the partly correct one of [[Galton, Francis|F. Galton]] and H.W. Watson by over 30 years and the
 
first subsequently correct one by over 80 (Heyde and Seneta, 1972; Bru, Jongmans and
 
first subsequently correct one by over 80 (Heyde and Seneta, 1972; Bru, Jongmans and
 
Seneta, 1992). (This theorem describes how the probability, $ q $, of extinction of a surname
 
Seneta, 1992). (This theorem describes how the probability, $ q $, of extinction of a surname
 
depends on the average number, $ m $, of male children per male parent. If $ m \leq 1 $
 
depends on the average number, $ m $, of male children per male parent. If $ m \leq 1 $
 
then $ q=1 $, but if  $ m>1 $ then $ q<1 $, and so there is a positive probability of
 
then $ q=1 $, but if  $ m>1 $ then $ q<1 $, and so there is a positive probability of
survival of surname.) In a letter to Quetelet (q.v.) of 21 April 1846, Bienaym&eacute;
+
survival of surname.) In a letter to [[Quetelet, Adolphe|Quetelet]] of 21 April 1846, Bienaymé
 
confides that his
 
confides that his
 
everyday work and the state of his health do not permit him complete preparation of his
 
everyday work and the state of his health do not permit him complete preparation of his
 
writings for publication, and that he works seriously on applications which are of
 
writings for publication, and that he works seriously on applications which are of
 
interest to both of them.  His ill-health, especially his trembling hands, were to
 
interest to both of them.  His ill-health, especially his trembling hands, were to
plague him to the end of his life.  (Quetelet, born the same year as Bienaym&eacute;, had
+
plague him to the end of his life.  (Quetelet, born the same year as Bienaymé, had
 
shortly before the letter paid a visit.  Their contact was to
 
shortly before the letter paid a visit.  Their contact was to
continue, with Bienaym&eacute;'s last letter to Quetelet dated September 1871).
+
continue, with Bienaymé's last letter to Quetelet dated September 1871).
  
In 1848 Bienaym&eacute; lost his job in the Ministry of Finances for political reasons
+
In 1848 Bienaymé lost his job in the Ministry of Finances for political reasons
 
associated with the changes of regime.  Shortly afterwards he was asked to give some
 
associated with the changes of regime.  Shortly afterwards he was asked to give some
lectures on probability at the Facult&eacute; des Sciences, Paris.  Again due largely to
+
lectures on probability at the Faculté des Sciences, Paris.  Again due largely to
politics the Chair for probabilities was finally given to Lam&eacute; who began
+
politics the Chair for probabilities was finally given to Lamé who began
 
his course in November, 1850, and spoke thus on 26 April, 1851:
 
his course in November, 1850, and spoke thus on 26 April, 1851:
  
 
<blockquote>
 
<blockquote>
It is my pleasure to count among my friends a savant (M. Bienaym&eacute;) who today,
+
It is my pleasure to count among my friends a savant (M. Bienaymé) who today,
 
almost alone in France, represents the theory of probabilities, which he has cultivated
 
almost alone in France, represents the theory of probabilities, which he has cultivated
 
with a kind of passion, and in which he has successively attacked and destroyed errors.
 
with a kind of passion, and in which he has successively attacked and destroyed errors.
Line 66: Line 65:
  
 
<!-- \noindent -->
 
<!-- \noindent -->
Finally Bienaym&eacute; was reinstalled in August 1850 as "Inspecteur
+
Finally Bienaymé was reinstalled in August 1850 as "Inspecteur
g&eacute;n&eacute;ral des finances, charg&eacute; du service des retraites pour la vieilesse et
+
général des finances, chargé du service des retraites pour la vieillesse et
des soci&eacute;t&eacute;s des secours mutuels".  Although he finally resigned in April 1852,
+
des sociétés des secours mutuels".  Although he finally resigned in April 1852,
 
his applied statistical interests were continued in the context of the Paris Academy of
 
his applied statistical interests were continued in the context of the Paris Academy of
Sciences (to which he was elected as "acad&eacute;micien libre'' in July, 1852), where
+
Sciences (to which he was elected as "académicien libre'' in July, 1852), where
 
he was referee for 23 years for the Prize of Statistics of the Montyon Foundation, the
 
he was referee for 23 years for the Prize of Statistics of the Montyon Foundation, the
 
highest French award in the area.  His eminence for such a role was enhanced by the
 
highest French award in the area.  His eminence for such a role was enhanced by the
Line 78: Line 77:
 
public domain.
 
public domain.
  
The period 1851-1852 also contains Bienaym&eacute;'s early contacts with J.J. Sylvester
+
The period 1851-1852 also contains Bienaymé's early contacts with J.J. Sylvester
(1814-1897) and Chebyshev (q.v.), and his contribution to the enhancement of their
+
(1814-1897) and [[Chebyshev, Pafnutii Lvovich|Chebyshev]], and his contribution to the enhancement of their
 
international standing.  The contact with Chebyshev was to become particularly
 
international standing.  The contact with Chebyshev was to become particularly
 
significant.
 
significant.
  
For Bienaym&eacute;, Laplace's ''Th&eacute;orie analytique
+
For Bienaymé, Laplace's ''Théorie analytique
des probabilit&eacute;s'' of 1812 was the guiding light, and much of his work is concerned
+
des probabilités'' of 1812 was the guiding light, and much of his work is concerned
 
with elaborating, generalizing and defending Laplacian positions.  When the first
 
with elaborating, generalizing and defending Laplacian positions.  When the first
 
treatise on probability in Russian (Buniakovsky's ''Foundations of the Mathematical
 
treatise on probability in Russian (Buniakovsky's ''Foundations of the Mathematical
 
Theory of Probabilities'', clearly modelled on Laplace) appeared in 1846, one
 
Theory of Probabilities'', clearly modelled on Laplace) appeared in 1846, one
biographer of Buniakovsky claims that Bienaym&eacute; and Gauss both learned Russian in
+
biographer of Buniakovsky claims that Bienaymé and Gauss both learned Russian in
order to be able to read it.  (Certainly the linguistically gifted Bienaym&eacute; knew
+
order to be able to read it.  (Certainly the linguistically gifted Bienaymé knew
Russian.)  Bienaym&eacute; was passionate in the defence of scientific truth as he
+
Russian.)  Bienaymé was passionate in the defence of scientific truth as he
perceived it and of his friends such as Cournot (q.v.), to the extent of attacking
+
perceived it and of his friends such as [[Cournot, Antoine Augustin|Cournot]], to the extent of attacking
Cauchy (q.v.) and Poisson (q.v.).  J. Bertrand (1822-1900), author of ''Calcul des
+
Cauchy and [[Poisson, Simeon-Denis|Poisson]]. [[Bertrand, Joseph|J. Bertrand]] (1822-1900), author of ''Calcul des
Probabilit&eacute;s'', a powerful Macchiavellian figure, eventually helped `bury' Bienaym&eacute;'s
+
Probabilités'', a powerful Macchiavellian figure, eventually helped `bury' Bienaymé's
 
reputation by unjustified criticism.  Contributing to his being largely forgotten till
 
reputation by unjustified criticism.  Contributing to his being largely forgotten till
the 1960's were the facts that Bienaym&eacute; was modest as regards his own achievements, made
+
the 1960's were the facts that Bienaymé was modest as regards his own achievements, made
 
no great efforts to assert his priority, and was ahead of his time in mathematical
 
no great efforts to assert his priority, and was ahead of his time in mathematical
 
statistics.  He left no disciples, not being in academia; and wrote no book.
 
statistics.  He left no disciples, not being in academia; and wrote no book.
Line 101: Line 100:
 
his year of birth, at a conference in Paris, some 12 papers on his life and work were
 
his year of birth, at a conference in Paris, some 12 papers on his life and work were
 
presented, in the presence of representatives of the still flourishing family
 
presented, in the presence of representatives of the still flourishing family
Bienaym&eacute;.
+
Bienaymé.
  
 
It is appropriate to say something of the famous and useful
 
It is appropriate to say something of the famous and useful
Bienaym&eacute;-Chebyshev Inequality, more commonly known by Chebyshev's name
+
Bienaymé-Chebyshev Inequality, more commonly known by Chebyshev's name
alone.  Both Bienaym&eacute; in 1853 and Chebyshev in 1867 proved it for sums of
+
alone.  Both Bienaymé in 1853 and Chebyshev in 1867 proved it for sums of
independent random variables.  Bienaym&eacute;'s proof, the simple proof which we
+
independent random variables.  Bienaym"'s proof, the simple proof which we
 
use today, is for identically distributed random variables, treating the sample
 
use today, is for identically distributed random variables, treating the sample
 
mean $\bar X$ in its own right as a single random variable, and is within his  
 
mean $\bar X$ in its own right as a single random variable, and is within his  
best known paper ``Consid&eacute;rations \`{a} l'appui de la d&eacute;couverte de
+
best known paper "Considérations à l'appui de la découverte de
Laplace sur la loi de probabilit&eacute; dans la m&eacute;thode des moindres carr&eacute;s."  
+
Laplace sur la loi de probabilité dans la méthode des moindres carrés."  
 
Chebyshev's proof is for discrete random variables and is rather more involved.  
 
Chebyshev's proof is for discrete random variables and is rather more involved.  
Bienaym&eacute;'s paper of 1853 is reprinted in 1867 in Liouville's journal immediately
+
Bienaymé's paper of 1853 is reprinted in 1867 in Liouville's journal immediately
 
preceding the French version of Chebyshev's paper.  The aim of both authors was a general
 
preceding the French version of Chebyshev's paper.  The aim of both authors was a general
 
form of the Law of Large Numbers.  Eventually, in a paper presented at a
 
form of the Law of Large Numbers.  Eventually, in a paper presented at a
 
conference in France and published in Liouville's journal in 1874, Chebyshev
 
conference in France and published in Liouville's journal in 1874, Chebyshev
acknowledges Bienaym&eacute;'s priority, and extracts from Bienaym&eacute;'s approach what is
+
acknowledges Bienaymé's priority, and extracts from Bienaymé's approach what is
the essence of the ``Method of Moments".  Chebyshev in 1887 used this method to give an
+
the essence of the "Method of Moments".  Chebyshev in 1887 used this method to give an
 
incomplete proof of the Central Limit Theorem for sums of independent but not
 
incomplete proof of the Central Limit Theorem for sums of independent but not
 
identically distributed summands, his final and great achievement in probability theory.
 
identically distributed summands, his final and great achievement in probability theory.
This proof was then taken up and generalized by his student Markov (q.v.)
+
This proof was then taken up and generalized by his student [[Markov, Andrei Andreevich|Markov]].
  
 
In the context of one of the polemics between Markov and P.A. Nekrasov (1853-1924)  
 
In the context of one of the polemics between Markov and P.A. Nekrasov (1853-1924)  
in response to a statement by Nekrasov that the idea of Bienaym&eacute; is exhausted  
+
in response to a statement by Nekrasov that the idea of Bienaymé is exhausted  
 
within the works of P.L. Chebyshev, Markov says:
 
within the works of P.L. Chebyshev, Markov says:
  
 
<blockquote>  
 
<blockquote>  
 
quad The reference here to Chebyshev is misleading, and the statement of
 
quad The reference here to Chebyshev is misleading, and the statement of
P.A. Nekrasov that the idea of Bienaym&eacute; is exhausted is contradicted by a
+
P.A. Nekrasov that the idea of Bienaymé is exhausted is contradicted by a
 
sequence of my papers containing a generalization of the method of
 
sequence of my papers containing a generalization of the method of
Bienaym&eacute; to settings which are not even touched on in
+
Bienaymé to settings which are not even touched on in
 
the writings of P.A. Nekrasov.
 
the writings of P.A. Nekrasov.
 
</blockquote>
 
</blockquote>
Line 138: Line 137:
 
Weak Law of Large Numbers holds.  This paper was written to contradict an assertion  
 
Weak Law of Large Numbers holds.  This paper was written to contradict an assertion  
 
of Nekrasov that independence was a necessary condition for this law.  Thus  
 
of Nekrasov that independence was a necessary condition for this law.  Thus  
according to Markov, Bienaym&eacute; might well be regarded as playing a role in the  
+
according to Markov, Bienaymé might well be regarded as playing a role in the  
 
evolution of Markov chain theory.
 
evolution of Markov chain theory.
  
Line 144: Line 143:
 
Chebyshev.
 
Chebyshev.
  
To conclude, here is an extract from a letter written by Bienaym&eacute; on 5 April 1878,
+
To conclude, here is an extract from a letter written by Bienaymé on 5 April 1878,
 
just before his own death, to E.C. Catalan (1814-1894).  It is a testament, prophetic
 
just before his own death, to E.C. Catalan (1814-1894).  It is a testament, prophetic
 
and a guide for our own times, with a touch of the old fire so evident in his
 
and a guide for our own times, with a touch of the old fire so evident in his
Line 161: Line 160:
 
{|
 
{|
 
|-
 
|-
|valign="top"|{{Ref|1}}||valign="top"|  Bru, B., Jongmans, F. and Seneta, E. (1992). I.J. Bienaym&eacute;:  Family information and the proof of the criticality theorem. ''International Statistical Review'', '''60''', 177-183.  
+
|valign="top"|{{Ref|1}}||valign="top"|  Bru, B., Jongmans, F. and Seneta, E. (1992). I.J. Bienaymé:  Family information and the proof of the criticality theorem. ''International Statistical Review'', '''60''', 177-183.  
 
|-
 
|-
|valign="top"|{{Ref|2}}||valign="top"|  Centre d'Analyse et de Math&eacute;matique Sociales (1997).  ''Iren&eacute;e-Jules Bienaym&eacute;, 1796-1878''. Actes de la journe&eacute; organis&eacute;e le 21 juin 1996. C.A.M.S.-138.  S&eacute;rie ``Histoire du Calcul des Probabilit&eacute;s" No.28, 124 pp. (54 Boulevard Raspail, 75270 PARIS Cedex 06).   
+
|valign="top"|{{Ref|2}}||valign="top"|  Centre d'Analyse et de Mathématique Sociales (1997).  ''Irenée-Jules Bienaymé, 1796-1878''. Actes de la journée organisée le 21 juin 1996. C.A.M.S.-138.  Série ``Histoire du Calcul des Probabilités" No.28, 124 pp. (54 Boulevard Raspail, 75270 PARIS Cedex 06).   
 
|-
 
|-
|valign="top"|{{Ref|3}}||valign="top"|  Heyde, C.C. and Seneta, E. (1972). The simple branching process, a turning point test and a fundamental inequality: A historical note on I.J. Bienaym&eacute;.  ''Biometrika'' '''59''', 680-683.  
+
|valign="top"|{{Ref|3}}||valign="top"|  Heyde, C.C. and Seneta, E. (1972). The simple branching process, a turning point test and a fundamental inequality: A historical note on I.J. Bienaymé.  ''Biometrika'' '''59''', 680-683.  
 
|-
 
|-
|valign="top"|{{Ref|4}}||valign="top"|  Heyde, C.C. and Seneta, E. (1977). ''I.J. Bienaym&eacute; : Statistical  Theory Anticipated'', Springer, Berlin.  
+
|valign="top"|{{Ref|4}}||valign="top"|  Heyde, C.C. and Seneta, E. (1977). ''I.J. Bienaymé : Statistical  Theory Anticipated'', Springer, Berlin.  
 
|-
 
|-
|valign="top"|{{Ref|5}}||valign="top"|  Jongmans, F. and Seneta, E. (1993). The Bienaym&eacute; family history from archival materials and background to the turning-point test.  ''Bulletin de la Soci&eacute;t&eacute; Royale des Sciences de Li&egrave;ge'', '''62''', 121-145.  
+
|valign="top"|{{Ref|5}}||valign="top"|  Jongmans, F. and Seneta, E. (1993). The Bienaymé family history from archival materials and background to the turning-point test.  ''Bulletin de la Société Royale des Sciences de Liège'', '''62''', 121-145.  
 
|-
 
|-
|valign="top"|{{Ref|6}}||valign="top"|  Seneta, E. (1982). Bienaym&eacute;, Iren&eacute;e-Jules. ''Encyclopedia of  Statistical Sciences'' (S. Kotz and N.L. Johnson, eds.) Wiley, New York. Vol. 1, pp.231-233.
+
|valign="top"|{{Ref|6}}||valign="top"|  Seneta, E. (1982). Bienaymé, Irenée-Jules. ''Encyclopedia of  Statistical Sciences'' (S. Kotz and N.L. Johnson, eds.) Wiley, New York. Vol. 1, pp.231-233.
 
|-
 
|-
 
|}
 
|}

Latest revision as of 19:59, 7 March 2024

Copyright notice
This article Irenée-Jules Bienaymé was adapted from an original article by E. Seneta, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([http://statprob.com/encyclopedia/Irenee-JulesBienaymeBienayme.html StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.

Irenée-Jules BIENAYMé

b. 28 August 1796 - d. 19 October 1878

Summary. Bienaymé was a Civil Servant. A disciple of Laplace, he proved the Bienaymé-Chebyshev Inequality some years before Chebyshev, and stated the Criticality Theorem of branching processes completely correctly in 1845. His work on corrrecting the use of the Duvillard life table is perhaps his greatest achievement as statistician in the public domain.

Bienaymé was born in Paris but began his secondary education at the lycée in Bruges, then part of the French Empire. His father held a senior administrative position in this town before moving his family back to Paris. Bienaymé entered the école Polytechnique in 1815, but this institution was closed in 1816 due to the fall of the Empire and the return of the Bourbons. With the death of his father in 1816, he entered the Ministry of Finances and rose to the rank of Inspector General in 1836. While carrying out his responsibilities as public servant, he was to become a self-made scientist, publishing first on demography and actuarial matters, and then on mathematical statistics. He was elected to the Société Philomatique de Paris in January, 1838 and was active in its affairs. His contributions to its meetings were reported in the now-obscure newspaper-journal L'Institut, Paris, being reprinted at the end of the year in the collections Procès-Verbaux de la Société Philomatique de Paris - Extraits. Most of his publications in the period 1837 to 1845 appear in this medium, and are characterized, to the frustration of the reader, by lack of mathematical proofs for assertions sometimes far ahead of their time. The most startling of his contributions occurs in this way when he gives, in 1845, a completely correct statement of the Criticality Theorem for simple branching processes, which precedes the partly correct one of F. Galton and H.W. Watson by over 30 years and the first subsequently correct one by over 80 (Heyde and Seneta, 1972; Bru, Jongmans and Seneta, 1992). (This theorem describes how the probability, $ q $, of extinction of a surname depends on the average number, $ m $, of male children per male parent. If $ m \leq 1 $ then $ q=1 $, but if $ m>1 $ then $ q<1 $, and so there is a positive probability of survival of surname.) In a letter to Quetelet of 21 April 1846, Bienaymé confides that his everyday work and the state of his health do not permit him complete preparation of his writings for publication, and that he works seriously on applications which are of interest to both of them. His ill-health, especially his trembling hands, were to plague him to the end of his life. (Quetelet, born the same year as Bienaymé, had shortly before the letter paid a visit. Their contact was to continue, with Bienaymé's last letter to Quetelet dated September 1871).

In 1848 Bienaymé lost his job in the Ministry of Finances for political reasons associated with the changes of regime. Shortly afterwards he was asked to give some lectures on probability at the Faculté des Sciences, Paris. Again due largely to politics the Chair for probabilities was finally given to Lamé who began his course in November, 1850, and spoke thus on 26 April, 1851:

It is my pleasure to count among my friends a savant (M. Bienaymé) who today, almost alone in France, represents the theory of probabilities, which he has cultivated with a kind of passion, and in which he has successively attacked and destroyed errors. It is to his counsels that I owe a proper understanding...

Finally Bienaymé was reinstalled in August 1850 as "Inspecteur général des finances, chargé du service des retraites pour la vieillesse et des sociétés des secours mutuels". Although he finally resigned in April 1852, his applied statistical interests were continued in the context of the Paris Academy of Sciences (to which he was elected as "académicien libre in July, 1852), where he was referee for 23 years for the Prize of Statistics of the Montyon Foundation, the highest French award in the area. His eminence for such a role was enhanced by the fact that he had worked hard to correct the state of affairs where upto about 1837 many insurance companies in France had used the Duvillard life table to considerable financial advantage, and the correction is deemed by some as his greatest achievement in the public domain.

The period 1851-1852 also contains Bienaymé's early contacts with J.J. Sylvester (1814-1897) and Chebyshev, and his contribution to the enhancement of their international standing. The contact with Chebyshev was to become particularly significant.

For Bienaymé, Laplace's Théorie analytique des probabilités of 1812 was the guiding light, and much of his work is concerned with elaborating, generalizing and defending Laplacian positions. When the first treatise on probability in Russian (Buniakovsky's Foundations of the Mathematical Theory of Probabilities, clearly modelled on Laplace) appeared in 1846, one biographer of Buniakovsky claims that Bienaymé and Gauss both learned Russian in order to be able to read it. (Certainly the linguistically gifted Bienaymé knew Russian.) Bienaymé was passionate in the defence of scientific truth as he perceived it and of his friends such as Cournot, to the extent of attacking Cauchy and Poisson. J. Bertrand (1822-1900), author of Calcul des Probabilités, a powerful Macchiavellian figure, eventually helped `bury' Bienaymé's reputation by unjustified criticism. Contributing to his being largely forgotten till the 1960's were the facts that Bienaymé was modest as regards his own achievements, made no great efforts to assert his priority, and was ahead of his time in mathematical statistics. He left no disciples, not being in academia; and wrote no book. However, more recently interest has revived, and on the 200th anniversary of his year of birth, at a conference in Paris, some 12 papers on his life and work were presented, in the presence of representatives of the still flourishing family Bienaymé.

It is appropriate to say something of the famous and useful Bienaymé-Chebyshev Inequality, more commonly known by Chebyshev's name alone. Both Bienaymé in 1853 and Chebyshev in 1867 proved it for sums of independent random variables. Bienaym"'s proof, the simple proof which we use today, is for identically distributed random variables, treating the sample mean $\bar X$ in its own right as a single random variable, and is within his best known paper "Considérations à l'appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés." Chebyshev's proof is for discrete random variables and is rather more involved. Bienaymé's paper of 1853 is reprinted in 1867 in Liouville's journal immediately preceding the French version of Chebyshev's paper. The aim of both authors was a general form of the Law of Large Numbers. Eventually, in a paper presented at a conference in France and published in Liouville's journal in 1874, Chebyshev acknowledges Bienaymé's priority, and extracts from Bienaymé's approach what is the essence of the "Method of Moments". Chebyshev in 1887 used this method to give an incomplete proof of the Central Limit Theorem for sums of independent but not identically distributed summands, his final and great achievement in probability theory. This proof was then taken up and generalized by his student Markov.

In the context of one of the polemics between Markov and P.A. Nekrasov (1853-1924) in response to a statement by Nekrasov that the idea of Bienaymé is exhausted within the works of P.L. Chebyshev, Markov says:

quad The reference here to Chebyshev is misleading, and the statement of P.A. Nekrasov that the idea of Bienaymé is exhausted is contradicted by a sequence of my papers containing a generalization of the method of Bienaymé to settings which are not even touched on in the writings of P.A. Nekrasov.

The first paper which Markov lists, published in Kazan, is that in which Markov chains first appear in his writings as a stochastically dependent sequence for which the Weak Law of Large Numbers holds. This paper was written to contradict an assertion of Nekrasov that independence was a necessary condition for this law. Thus according to Markov, Bienaymé might well be regarded as playing a role in the evolution of Markov chain theory.

The Method of Moments, however, like the Inequality, has come to be ascribed to Chebyshev.

To conclude, here is an extract from a letter written by Bienaymé on 5 April 1878, just before his own death, to E.C. Catalan (1814-1894). It is a testament, prophetic and a guide for our own times, with a touch of the old fire so evident in his controversies.

You do not see then that everything in the world is only probabilities, or even just conjectures; and that in days to come all questions, more or less scientific, will be better understood, or even solved [in these terms] when sufficient education is given to minds capable of it by it good teaching of probability. I don't say to all minds, as there are weak intellects, and a great number of fools...


References

[1] Bru, B., Jongmans, F. and Seneta, E. (1992). I.J. Bienaymé: Family information and the proof of the criticality theorem. International Statistical Review, 60, 177-183.
[2] Centre d'Analyse et de Mathématique Sociales (1997). Irenée-Jules Bienaymé, 1796-1878. Actes de la journée organisée le 21 juin 1996. C.A.M.S.-138. Série ``Histoire du Calcul des Probabilités" No.28, 124 pp. (54 Boulevard Raspail, 75270 PARIS Cedex 06).
[3] Heyde, C.C. and Seneta, E. (1972). The simple branching process, a turning point test and a fundamental inequality: A historical note on I.J. Bienaymé. Biometrika 59, 680-683.
[4] Heyde, C.C. and Seneta, E. (1977). I.J. Bienaymé : Statistical Theory Anticipated, Springer, Berlin.
[5] Jongmans, F. and Seneta, E. (1993). The Bienaymé family history from archival materials and background to the turning-point test. Bulletin de la Société Royale des Sciences de Liège, 62, 121-145.
[6] Seneta, E. (1982). Bienaymé, Irenée-Jules. Encyclopedia of Statistical Sciences (S. Kotz and N.L. Johnson, eds.) Wiley, New York. Vol. 1, pp.231-233.



Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.

How to Cite This Entry:
Bienaymé, Irenée-Jules. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bienaym%C3%A9,_Iren%C3%A9e-Jules&oldid=39178