Board of the Foundation of the Scandinavian Journal of Statistics
Scandinavian Statistics, Some Early Lines of Development
Author(s): Tore Schweder
Source: Scandinavian Journal of Statistics, Vol. 7, No. 3 (1980), pp. 113-129
Published by: Blackwell Publishing on behalf of Board of the Foundation of the Scandinavian Journal of
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Scand J Statist 7:113-129, 1980
Scandinavian Statistics,
Some Early Lines of Development
TORE SCHWEDER
University of Troms0
Received August 1979
ABSTRACT. The history of Scandinavianstatistics (pre 1920)
is sketched. The exposition is journalistic.For 10 early Scandinavian statisticians some background material together with
a rough summary of their contributionis presented. A drawn
portrait and a selected bibliographyis also presentedfor each.
this work. Anders Hald, Herman Wold, Lars Erik
Oller and others deserveparticularthanks for their
help at the outset.
Key words: History of statistics, least squares, cumulants,
stochastic processes, survey sampling
A brief historicalsurvey
We can trace three distinct main lines of development in early Scandinavianstatistics. The oldest
one may be termed social statistics: population
Preface
statistics and demography, statistical sociology
The following is based on the exhibition with the and "official" statistics with survey sampling.The
abovetitle,whichwaspresentedat the 11thEuropean second line is that of mathematicalstatisticsand its
meeting of statisticians,Oslo, 1978. The aim of the applications: regression, analysis of variance,
exhibition was not to present a complete picture series expansions, cumulants and other general
of the early history of statisticsin Scandinavia,but theory. Modelbuilding and applications of theorather to throw some light on some of our more retical concepts was undertaken in the fields of
outstanding predecessors.The following "journa- insurance,forestry, astronomy, biology and social
listic" exposition is based on what I have come sciences.The final main line was that of stochastic
across in biographies,obituariesand the like and, processes:Poisson process,risk theory and queuing
on the study of some of the works mentioned in theory, and its applicationto insuranceand engithe bibliography.In addition to the coarse descrip- neering.
tion of the work of the variousauthorsI have tried
to place their work against a culturaland personal Social statistics
background.I hope the reader will share my view The developmentof social statistics was basically
that this is of interestin additionto the chronology nonmathematical.It startedwith Wargentinand the
and priority of the various contributions. My Swedish population statistics, produced regularly
presentationis that of an amateur in the history from 1749 - the world's oldest.
of science, but despite its briefness, omissions,
Someearlierpopulationnumberswerefor military
biases and other shortcomings,I hope it will be of reasons kept as state secrets and not published.
The achievementsof Wargentinand coworkerswere
some value.
Below follows a brief historical survey of early not so much in the theoreticalrealm but more in
Scandinavianstatistics,which except for Lindeberg making the value of population statistics underis pre 1920. In the next section I have raised some stood, in establishingan administrationfor populaquestions and put forward some views. Then my tion enumerationand in publishinginterestingand
10 favourite early Scandinavian statisticians are reliable population statistics. From the time of
presented in alphabeticalorder. The portraits are Wargentin,official statistics in the area of demodrawn by my father Carl Schweder.In the selected graphy and also economics was steadilyimproved
bibliographiesI have included what seems to me in Scandinavia.
to be of primaryinterestto statisticians.Secondary
The area of statistical sociology was opened by
readingis also included,some of which gives com- Eilert Sundt, a theologist who devoted his life to
the study of the underpriviledgedin Norway. He
plete bibliographies.
I want to thank the University library in Oslo collected statistics on a number of sociological
and Troms0 for the help I receivedin carryingout variablespreviouslyneglectedand he made impor8-801928
Scand J Statist 7
114
T. Schweder
tant contributionsto demography.His researchwas
characterized by good design and analytical
methodology. As his contemporary Karl Marx,
Sundt wrote for the common man, often in a
poetic style.
Throughout the 19th century statistical bureaus
were organized to collect and present official
statistics.It was felt that importantquestions, particularly of a social statistical nature, would be
impossible to answer if only the method of total
enumerationwere used. Kier, head and originator
of the Norwegian CentralBureau of Statisticshad
well documented stratified sample surveys carried
out in the 1890's. He argued strongly to have the
method internationallyacceptedand furtherinvestigated.
Stochastic processes
Important areas of the young field of stochastic
processeswere developedin Swedenand Denmark.
In 1903 the actuaryLundbergpublisheda remarkable thesis in which he worked out a theory for
Markov jump processes. His aim was to establish
a collective risk theory of insurance.Independently,
in 1909, the Copenhagen mathematican Erlang
was led to the Poisson process and its relatives.
His area was that of communicationengineering
and he is well known as the founder of queueing
theory.
Both the two men had a sound mathematical
background, and they were early engaged in
practicalwork. Lundbergstartedhis long insurance
careerat the age of 21, and Erlangwas hired by the
Copenhagen Telephone Company. In addition to
the mathematicalfascination,their ground-breaking
Mathematical statistics with applications
work was inspired by the practical problems they
The development of mathematical statistics in were faced with.
Scandinaviastartedin Copenhagen,actually in the
Erlang's works were immediately recognized
Mathematisk Forening (Mathematical Associa- and put to use. Lundbergwas also judged as briltion). A strong Danish school of statisticsevolved liant-but impossibleto understand.It took 30 years
and it may be argued that it rivalled the London before the statistical community really started to
school as the leading center of statisticsat the turn digest the conceptualmethodologicalachievements
of the century.The backgroundof the Copenhagen of Lundberg.
school was formed by Gauss and his theory of least
squaresand normal distribution.
Out of pure intellectual interest, a member of Historicalperspective
Parliamentand professor of German, Oppermann,
picked up the Gauss theory. The young Gram Our Scandinavianhistory is, of course, part of the
refined Oppermann's ideas of linear space and broader European history. The cultural contacts
orthogonalizationaiming at a theory of approxi- with continental Europe and Britain were strong
mation. In the hands of the astronomerThiele the throughout the period of our interest and this is
theory ripened into a mature and modernbody of reflected in the Scandinavianhistory of statistics.
science featuring the basics of regression,analysis The flux of ideas from Europe is quite evident in
of variance, asymptotic expansions, semi invari- the work of Wargentin-he corresponded with
ants (cumulants)and elements of estimation and Siissmilch,Deparcieux,Price; in that of Sundt and
testing theory. In 1889 Thiele publishedthe (first?) Kiaer-the latter was a very active member of the
textbook of mathematicalstatistics with the well- newly founded ISI; and in the Copenhagenschool
chosen title: Almindelig Iagttagelseslxre (General with their dependenceon Gauss and the German
mathematicaltradition.Both Lundbergand Erlang
theory of observation).
Parallelto theirtheoreticalwork, the Copenhagen relied on the mathematicaltradition,but as to their
statisticianswereeagerlyapplyingmathematicaland originalcontributionsin stochasticprocessesit is not
statistical methods to problems of practical im- straightforwardto trace any direct influencesfrom
portance.Oppermannand Gram were interestedin abroad.
How about the flux of ideas the other way?
forestry, Thiele of course in astronomy, and they
What was the impactof Thiele's1903 Englishtranswere all deeply involved in insurance.
Copenhagenremainedthe centerof Scandinavian lation: Theory of observations? Did the young
statistics. After 1900 mathematical statistics also Fisher read Thiele and thereby get inspirationfor
dispersed to Sweden and later to Finland and his ANOVA and his cumulants which was a reinNorway. In Lund the professor of astronomy vention of Thieles semiinvariants?What about
Charlierworkedto spreadstatisticalideasto various Lundberg?He probably did not have much direct
fields of applications. So did the Finnish mathe- impact;why was it necessarywith a Cramerto make
maticianLindeberg,who is known for his work on the contribution of Lundberg appreciated?There
are many questionsto which I have no answers,but
the CentralLimit Theorem.
Scand J Statist 7
EarlyScandinavian
statistics 115
I think it would be of great interest if someone
would trace the history of these statisticalideas.
Besides this subject we have the equally important subject of the sociology of science. What
were the forces behind the scientific developments
-was there any technical, economical or bureaucratical need for the results obtained? Did the
ideas mainly springout from an academictradition
or was the contact with other sectors of society of
importance?Without exception the actors on the
statisticalscene presentedin this paper had a solid
University training. However, the majority had
their occupation outside the University,and only
Lindebergworked in a mathematicaldepartment.
Wargentinand Kiaerworked mainly in the interest
of an enlighted state and bureaucracy, Sundt
worked for the enlightenmentand the interest of
the underprivilegedout of own moral and basic
politicalreasons.The initiatingforcesbehindOppermann, Gramand Thieleseem to have been basically
mathematicaland intellectual,but theirinterestand
engagementin insurance, forestry and astronomy
no doubt representedinspirationsand contributed
to the molding of their work. Also Lundbergand
Erlang were mathematiciansat the outset who
broughttheirknowledgeand abilitiesout in the field
(insuranceand communicationengineering)and had
it exposed to practicalneeds. This contact not only
influencedtheirchoice of area of study,but also had
a strong impact on the way they carriedout their
researchand the results they obtained.
It may also be noted that all, maybeexceptSundt,
were regardedas prominentand successfullmen of
their time. Sundt's researchwas too radical to be
sufficientlyappreciated,but for the rest it seemsthat
particularlytheir applied mathematicalwork was
highly appreciatedby their society.
In summary,earlyScandinavianstatisticsemerged
as a basicallyappliedsciencerooted in mathematics
and the broaderEuropeanintellectualtradition.Its
practitioners were respected members of society
and the achievementswere of a high, some times
history-makingstandard.
Scand J Statist 7
116 T. Schweder
Charlier, Carl Wilhelm Ludwig (1861-1934)
Charlierwas professorof astronomyin Lund. Early
he was mainly occupied with theoretical astronomical questions. Later he worked with stellar
statistics and, in particular, with the spatial
distributionof helium stars.
At the age of 43 Charlierturnedto statisticsand
after 1904 he functionedmore or less as a professor
of statistics.A chair of statisticswas establishedin
Lund in 1924, mainly on Charlier'sinitiative.
Charlierhad regular contacts with Copenhagen
Scand J Statist 7
and must have known the works of Thielewho also
was a professorof astronomy.In Thiele'stextbook
the expansion of Gram was discussed at length,
Without referring neither to Gram nor Thiele,
Charlierpublishedthe same expansionin 1905. He
based his exposition on Fourier series and (improperly)on the inversionformula.
Charlier worked to disperse statistical ideas to
other academic diciplines, mainly biology, and he
fitted probabilitymodels to a numberof data sets.
Early Scandinavianstatistics 117
*~~~~~~~~~~~~~~~~
,.-e
Erlang,AgnerKrarup(1878-1929)
With a solid background in mathematics and
physical science, Erlang was in 1908 hired by
J. L. W. V. Jensen (Jensen'sinequality)to apply
probabilitymethods to the problemsof the Copenhagen Telephone Company. The two met in the
MathematicalAssociation.At that time the manager
of the Companyhad alreadypublishedtwo papers
employing probability arguments to telephony.
Erlang continued working with the Company for
the rest of his life.
In orderto find the rightnumberof circuitsof an
automatic telephone exchange with a given traffic
load and to solve other problemsin communication
engineering, Erlang introduced the Poisson processes and other related stochastic processes. He
establisheda conceptualand methodologicalframework of queueing theory. Prior to 1908 he was
consulted by Jensen, and he was able to publish
this major achievement as early as in 1909. In
solving for the waiting time distributionand other
properties of his models, Erlang considered the
stationaryaspects of the system. He called this the
method of "statistical equilibrium",and used it
efficiently.In this mannerErlangwas able to present
quite brief and elegant arguments for his results.
The time was ripe for Erlangscontributions.His
results were promptlyput to use both in Denmark
and abroad. His 1917 paper was translated into
English and German in 1918 and into French in
1922. The engineeringcommunity was so eagerly
waitingfor such resultsthat a Frenchand an American engineer studied Danish to be able to read
Erlangsworks as they appeared.
On his mother's side Erlang was of the great
Krarup family. Since the time of Tycho Brahe,
membersof the family held chairsat the University
of Copenhagen. Traditionally the male members
of the family were clergymenand the females were
wives of clergymen.Erlang'sfather was however a
schoolteacher. As Galton did in 1873, Erlang
publishedin 1929the problemof findingthe probability of a surname going extinct. Unlike the
readershipin London55 yearsearlier,that in Copenhagen was able to deal with the problem and the
journal received three solutions, two of which
were complete. The same year Erlang died, leaving
no children.
Scand J Statist 7
118 T. Schweder
Gram, Jorgen Pedersen (1850-1916)
At the outset, Gram was a Copenhagenmathematician. Later he became interestedin forestryand
insurance,but he maintained his mathematicalinterest. Gram was managingdirectorof a non life
insurancecompany which he founded and he was
involved in the life insurancecompanyHafnia togetherwith Oppermannand Thiele.
In his thesis of 1879, later publishedin Crelle's
journal, Gram worked out a theory of function
spaces. Following Oppermann (and Gauss), he
developed stepwise regressionby successiveorthogonal projections.By lettingthe numberof observations increaseto infinity,he was led to the concepts
of L2 distance,innerproductand orthogonalityfor
Scand J Statist 7
the space of continuousfunctions.He also obtained
the Pythagoras theorem for the projection on a
space spanned by a set of orthogonal functions.
Gram consideredthis a theory of approximations.
Becauseof a lack of measuretheory, his characterization of the space spannedby an orthogonalbasis
is not completely satisfactory.But except for the
notion and results on completenesshe laid out the
basics of Hilbert space theory.
Among the three systemsof orthogonalfunctions
whichGramconsideredwe find the derivativesof the
normal curve D'(e-'O)n = 1, 2, .... Linear approximation by these functionsgive the Gram-(Charlier)
expansion.
EarlyScandinavianstatistics 119
.. ....
~
..i.
~
~
"...,
......-: Z f
..........
rs Nicolai
(1838-191.
)
Kier.,AndersNicolai (1838 1919)
The name of Anders Kiar is intimatelyconnected
with the Central Bureauof Statisticsof Norwayand with random survey sampling. As a young
lawyer he came to the StatisticalOffice of the Department of the Interior. On his initiative this
office was reorganized in 1873 as the Central
Bureau of Statisticswith Kiwr as director,a position which he held for 46 years.
Kiaerpersonallyled a number of the statistical
investigationsof the Bureau in the fields of economics, sociology and demography,and he normally wrotethe introductionsto the variousstatistical publications.
The standardmethodof the time was that of total
enumeration.It was howeverclear to Kier and his
coworkerJacobNeumanMohnthatmanyquestions,
particularlyof a social statistical nature, would
remain impossible to answer if only this method
was to be used. They found surveysamplingto be
necessary to get information of sufficient depth.
Mohns investigation Om husmandsklassen(On
the classof crofters),Norskrettstidende
1-2, 1880,and
later studies wereforerunnersof Kikr's 1891investi-
gation of personal income and capital, based on
quasi random sampling. In 1895 Kier used a
method of proportionalstatifiedrandomsampling.
KiaDrwas not a mathematician(nor was Mohn)
and he did not formally develop his ideas of the
"representativemethod of sample surveys". However, he described in detail how the sample was
drawn and noted in one case that "the sampling
mechanism is so haphazard and random relative
to the populationthat one may assumethat it does
function in the same way as a lottery".
Kitr found it hard to convince the 1895 ISImeetingthat the "representative
method"was useful.
It was argued that although the method now and
then had given interestinginformation,its principle
was so muchin oppositionto "la statistiqueserieuse"
that the "imperfect"method should not be granted
equal status with the statisticalideal.
The ISI was foundedin 1885. Kihr was an active
member of the organizationand he was the host
for the fifth ISI meeting in Oslo (then called
Kristiania)in 1899.
Scand J Statist 7
120
T. Schweder
Lde 8........
Jal
a
Lindeberg,Jar! Waldemar(1876-1932)
Lindebergstudied mathematicsin Helsingforsand
Paris. From 1900he publishedworks on differential
equationsand the calculusof variationsand in 1905
he was appointed adjunkt in mathematicsat the
Universityof Helsingfors.Because of his scientific
merits he could easily have been promoted to
professor, but he refused such proposals. He was
afraid of having more responsibilities,and being
unable to spend the whole summerat his beloved
resort place.
At the age of 40 Lindebergbecame interestedin
probabilityand statistics.In 1920 he publishedhis
first work in this area, the well known "LindebergLevy theorem".Here he introducedthe technique
of adding a normal variate to the sum of independent variatesto smooth the distributionof the
sum and make the Taylor expansionwork.
Scand J Statist 7
In 1926 Lindeberg defined his correlation percentagewhich is nothing but Kendall'sr. He calculated the first two moments, but did not discussits
distributionany further.He proposedto use normal
scores when calculating the product moment
correlation.
Lindebergtook part in the discussionof the line
transect method in forestry. When deriving the
numberof transectsnecessaryto obtaina sufficiently
narrow confidenceintervall,he in 1926 apparently
rediscoveredthe Student distribution.
Lindebergwas an active memberof the actuarial
society and he sat on the board of an insurance
company.He was frequentlyconsultedon statistical
questionsby researchersin areas like forestry,biology, medicineand linguistics.
EarlyScandinavianstatistics 121
A
e..
Lundberg, Ernst Filip Oscar (1876-1965)
Natural sciencesand chemistrywas what interested
Lundbergthe most. Headingfor a careeras a school
teacher, but being a poor student,Lundbergchose
to study mathematicsinstead of chemistryto cut
down on study time.
At the age of 22 Lundbergbegan to work for a
life insurancecompany. The businesspolicy of the
company was not a lucky one and it was next to
ruin after a few years of operation.Lundbergquit
his job for this reason. His next job was in the life
insurance company De F6renade with which he
worked for half a century, most of the time as
managing director. Lundberg'snew company was
however also in difficultiesand got into financial
trouble. He decided to take up his studies to become a teacherbecausehe figuredthe school to be
a safer businessthan insurance.
For his thesiswork,Lundberglooked for an "area
of limitedliteratureand in whichit was not required
to masterthe methodologyof mathematicalresearch
too profoundly.To me the mathematicalrisk theory
appearedto be such an area." Another reason for
choosing this area of research was probably his
personalexperiencewith the risky business.
Lundberg'sfundamentalUppsala thesis appeared
in 1903. Instead of following the individual cases
he considered the risk process of the whole collective: the stochastic claims coming in at random
points in time. For this marked Poisson process
Lundbergdevelopeda substantialamountof theory
including the forward equation, the concept of
operational time, asymptotics and Berry-Esseen
type bounds for the cumulativerisk process.
For a degenerateclaim distribution,the Poisson
distributionwas found to be a simple solution to
the forwardequation.
In later papers various modificationsof the risk
process were introduced, and problems of level
crossing,extremevalue and ruin were made subject
to more detailedstudy.
Because of a condensed style and a difficult
subject. Lundberg'sworks got the reputation of
being impossibleto understand.Unlike Erlangwho
was immediatelyaccepted, Lundberghad to work
alone and wait some thirty years before his fundamentalideas were pickedup by Cramerand others.
Scand J Statist 7
122 T. Schweder
Oppermann,Lv
ek
d
n
8
Oppermarnn,
LudvigHenrikFerdinand(1817-1883)
Oppermannstudied language, was a schoolmaster
and later a professor of German. He also studied
forestryaimingat a careeras "skovridder"(forester)
as his father. He was a memberof the Danish Parliament for 12 years.
Besides his daily work, Oppermannhad a living
interest in mathematics.He favoured Archimedes,
Newton and Gauss.At the age of 28 he publisheda
textbookon geometrywhichwas found too difficult
to be put in use. This text was later "modified"by
ProfessorSteen, but the neccessityof this modification remainedimpossiblefor Oppermannto understand. He never felt part of "the official mathematics".
Oppermann studied Gauss very carefully, in
particularhis method of least squares which he
complainedwas not developedany further.In 1863
he publishedtwo remarkablepaperssigned "En dilettant" (A dilettant).The first one "En foresp0rgsel" was a 9 line piece requestingthe distributionof
the empiricalvarianceof a normal sample.
The other paper, "Minimumsproblemer"was
Scand J Statist 7
an impressively concise presentationof the least
squares method. Oppermannused in essence the
fundamental notion of linear space of vectors
u, v ... with inner product [uv], orthogonality
between vectors and linear subspaces. And he
turned the Gauss elimination procedure into the
Gram-Schmidt orthogonalizationprocedure. This
paperwas apparentlyhardto readwhenit appeared,
but togetherwith subsequentverbalcommunication
it had a greatimpact on Gram and Thiele and their
school of statisticians.
As most of the subsequentDanish statisticians,
Oppermannwas engaged in life insurance.He was
Mathematicaldirectorof a life insurancecompany.
In the 1860's Oppermannemployed least squares
methods to smooth mortality tables. He kept his
mortality functions a secret for many years, but
after Thiele had guessed the functional form from
the graphs,he turned more communicative.
The empirical cumulative distributionfunction
was used by Oppermannto check the assumption
of normality.
EarlyScandinavianstatistics 123
*
-
-'~~~~~~~~-~~~~*
--'
(817-8-
-.-MR-'-
-
As a young theology student, Eilert Sundt met
HenrikWergeland,our Norwegianpoet of freedom.
He was inspiredby Wergelandand felt a desire to
be challengedby a "high and worthy aim" in his
spirit. This he found in sociological research-in
describingand making understoodthe nature and
causes of the misery of various underprivileged
groups, but also to bring forth their prideand
worth.
As a Sundayschool teacherin a prisonSundtmet
a number of gypsies. Among them old men who
werenot put in for any crimebut werekept for years
to be taughtreligionand preparedfor confirmation.
This moved Sundt so much that he gave up his
promisinguniversitycareerand decided to investigate the conditions of this out group. He made a
two month trip on foot across the countrybut did
not meet a single gypsy. He saw howeverso much
misery that he decided to devote his life to the
study of the common man. His books, writtenin a
poetic style but based on solid statistics covered
areaslike gypsies,the state of morality,temperance
conditions, housing and sanitary conditions, the
conditionsof labour-,peasant-,fishery-and mining
populations,demographyand more anthropological
areas like the home industryof women.
In addition to the scanty official statistics
available,Sundt made use of statisticshe collected
by having clergymenand school teachersreport on
their districts. He also conducted an interview
surveyof all the familieswith school childrenof the
communityPipervikenand Rusel0kbakken,a labour
class suburbof Christiania(Oslo).
For severalmonths each year for a period of ten
yearsSundtwalkedthroughvalleysand along shores
to gather first-handinformationon the people he
studied. On his travels he collected much original
Sunt,
ilet
Eilert (1817-1875)
~~~~~~~~~Sundt,
and interestingdata and he was inspiredfor further
studies.
Sundt's research was characterized by good
design and logic. He collected his data with some
quite clear hypotheses in mind, hypotheses which
grew out of painstakinggroundwork and which he
stuck with throughoutthe analysis. The hypotheses
were informally tested by comparingdistributions,
not only mean values.
By cross-classificationSundt was able to expose
a varietyof possiblebiasesof his reporters(teachers,
clergymen).When using an interviewerhe kept his
hypotheses secret to avoid bias. Spurious correlations, and possibleexternalfactorswere sought and
Sundt was often led to consider two- or three-way
tables.
It is regrettablethat none of Sundt'smany works
have been translated.He must be regardedas one
of the first modern sociologists. After twenty years
of researchthe stingy Storting(Parliament)was no
longer willing to fund further research. Jaabek
(with the nicknameNeibekk)arguedthat since such
researchwas not undertakenin any other country
it could not be of any value.
But the Stortingdid make Sundt's researchpossible by direct yearly funding for almost twenty
years. One of the reasonswas the fear in the ruling
class of the risingsocialismaround 1848.One hoped
that the theologistSundtcould help dam up for this
movement.Even though Sundthimselfwas strongly
against MarcusThraneand his socialism,the longterm effects of Sundt's writing have been positive
for the left in Norway. Sundt himself founded and
led the Christiania (Oslo) Workers Association,
and must be regardednot only as an outstanding
statistician and a father of sociology but also a
father of Norwegiansocial democracy.
Scand J Statist 7
124 T. Schweder
T
(
--
. I..
Thiele, ThorvaldNicolai (1838-1910)
Thiele studied astronomyand became professorin
Copenhagen. Because of mathematicalinterestsand weak eyes, he worked mainly with theoretical
astronomy.
At the age of 34 he took part in establishingthe
life insurance company Hafnia in which both
Oppermann and Gram were engaged. He later
founded the Danish ActuarialSociety.
Thiele's interestsin mathematics,astronomyand
insuranceled him naturallyto statistics.In 1889 he
publishedhis text AlmindeligIagttagelseslerewhich
in revisedform appearedas Theoryof observations
(1903) in a "barbarousEnglishtranslation(Hilary
was
Seal). The theory of Gauss-Oppermann-Gram
here developedto a maturebody of science.
Cumulantswereinventedby Thiele,he calledthem
half invariants.They were used both for estimation
purposesand for theoreticalarguments.How Thiele
happened to understand that the cumulants Ai de-
fined by
t
/t
cakbeing the kth moment, had
Ar(E akXk) = E akAr(Xk)
Scand J Statist 7
the property
for independent X1, ..., X. is a mystery. But in 1889
he used this as an argumentfor the CentralLimit
theorem.
Thielemade a clear distinctionbetweenempirical
and theoreticaldistributions(he called them laws of
actual versus presumptiveerrors).He discussedthe
sampling propertiesof his estimates and adjusted
them for bias. For least squares analysis he
stressedthe assumptionsof normality,independence
and equal (but known) variance.
By orthogonalization it was known how to
partition the sum of squares.This Thiele used for
"summary critisism", in effect hypothesis testing
about the whole or a part of a linear model. Only
the first two momentsof the appropriateX2distribution was used, tail probabilitieswerenot considered.
In his 1889text, a thoroughlyworked-outexample
fromastronomyof a two way ANOVA was included.
This was however replaced by more "pedagogic"
examplesin the English edition.
In addition to the ANOVA-summarycritisism,
Thiele proposedresidualanalysisindludingresidual
plots, runs tests and sign tests. By inspectingthe
residual plot, left-out-regressorsmay be revealed,
but it is warnedagainstoverfittingthe model. Also
here the 1889 edition is more interesting.
EarlyScandinavianstatistics 125
Pehr W
Wargenm,,
(1717......1783).
Wargentin, Pehr Wilhelm (1717-1783)
At the age of 11 Wargentinexperienceda lunar
eclipse. That it was possible to predict this event
to the hour, puzzles him so much that he decided
to study astronomy. In Uppsala Celsius was his
teacherand Linn6his friend.He did suchremarkable
work on the satellitesof Jupiterthat, at the age of
24, he was offered the chair after Celsius. He
balked because he would rather be a "respectable
school teacherthan a mediocreprofessor".
In 1749 Wargentinwas appointed secretaryto
the then 10 years old Swedish Royal Academy of
Science. He kept this position to his death. The
responsibilities included: to edit the quarterly
proceedings,to edit various almanacs,to establish
a libraryand to be the librarian,to take care of the
correspondence(he receivedmorethan4 000 letters),
daily to take astronomicaland meteorologicalobservations,to establishan astronomicalobservatory
-and to raise much needed money.
In addition to his regular duties as secretary,
Wargentinkept working on the Jupiter problem.
He becamean activememberin variouscommissions
dealing with: constructingthe Trollhattanchannel,
making maps of the coastal waters of Sweden,
revising the Bible-and with establishingnational
populationstatistics.
From 1686 the clergymenwere to keep records
of the inhabitantsof theirparishes.In 1749a central
statisticaloffice was established,and from that year
regularnationalpopulationstatisticswere produced
in Sweden.Fearingthatenemiesshoulddiscoverhow
small the population was, the numberswere kept
a state secret until 1757.
The records produced by the clergymenturned
out to be of varyingquality.To improvethe motivation for this work, Wargentinproposed in 1753 to
have Siissmilchs Die gdttliche Ordnung of 1741
translatedto Swedish.Wargentindid in fact know
the works of the leading demographersof the time:
Graunt, Halley, Kersseboom, Suissmilch,Deparcieux, Price, and he correspondedwith the latter
three.
To open the eyes of the public for the value of
population statistics in areas like medicine and
pension funds, and for the national goal of increasing the population, Wargentinwrote a series
of papers. Another motive was to persuade the
authoritiesto make the populationnumberspublic.
Wargentin covered most of the demographic
field. To smooth his mortality tables he averaged
the number of deaths over three year periods. He
studied the monthly variationof deaths and births
and he studiedmigration.He envisagedthe population as an age pyramid"in which the childrenform
the base and the old ones the top".
Scand J Statist 7
126
T. Schweder
Selected bibliographies
Charlier, Carl Wilhelm Ludwig
1905 Vber das Fehlergesetz. Ark. Mat. Astr. Fys. 2, no. 8.
Die zweite Form des Fehlergesetzes. Ark. Mat. Astr.
Fys. 2, No. 15.
1906 Researches into the theory of probability. Lunds Univ.
Irsskr., N.F. Avd. 2, 1, no. 5.
1908 Weiteres uber das Fehlergesetz. Ark. Mat. Astr. Fys.
4, no. 13.
1909 Die strenge Form des Bernoullischen Theorem. Ark.
Mat. Astr. Fys. 5, no. 15.
1910 Grunddragen af den matematiska statistiken. Lund.
Vorlesunguiberdie Grundziigeder matematischenstatistik. Hamburg, 1920.
Elements of mathematicalstatistics. Cambridge, Mass.,
1947.
1911 Researches into the mathematical theory of statistics.
Ark. Mat. Astr. Fys. 7, no. 17.
1912-14 Contributions to the mathematical theory of
statistics. Ark. Mat. Astr. Fys. 8-9.
1921 Loi des grands nombres. Scientia.
Introduction to stellar statistics. Hamburg.
1928 A new form of the frequency function. Lunds. Univ.
Arsskr., N.F. Avd. 2, 24, no. 8.
Secondary reading:
Cramer, H. (1972). Studies in the History of Probability and
Statistics XXVIII. On the history of certain expansion
used in mathematical statistics. Biometrika 59, 1, 205-7.
Sarndal, C. E. (1971). Studies in the History of Probability
and Statistics XXVII. The hypothesis of elementary
errors and the Scandinavian school in statistical theory.
Biometrika 58, 2, 375-91.
Both papers are reprinted in:
Kendall, M. & Plackett, R. L. (ed.) (1977). Studies in the
history of statistics and probability, vol. 2. London.
Erlang, Agner Krarup
Erlang's collected works appear in English translation in
Brockmeyer et al. (1948).
1909 Sandsynlighedsregning og Telefonsamtaler. Nyt Tidsskr. Mat. B: 20, p. 33.
Calcul des probabilities et conversations t6t6phoniques.
Revue gen&ralde l'Electricite 18, 1925, p. 305.
1917 L0sning af nogle Problemer fra Sandsynligheds regningen af Betydning for de automatiske Telefoncentraler. Elektroteknikeren 13, p. 5.
Solution of some problems in the theory of probabilities
of significance in automatic telephone exchanges.
The Post Office El. Eng. Jour. 10, 1918, p. 189.
Losung einiger Probleme der Wahrscheinlichkeitrechnung von Bedeutung fur die selbstatigen Fernsprechamter. ElektrotechnischeZeitschr. 39, 1918, p. 504.
Solution de quelque problemes de la theorie des
probabilites presentant de l'importance pour les bureaux t6l6phoniques automatiques. Annales des
Postes, Telegraphes et Telephones 11, 1922, p. 100.
1920 Telefon - Ventetider. Et stykke Sandsynlighedsregning. Mat. Tidsskr. B: 31, p. 25.
Calcul des probabilites et conversations t6l6phoniques.
Revue generale de l'Electricite 20, 1926, p. 270.
1922 Sandsynlighedsregningens Anvendelse i Telefondrift.
Forste nordiskeElektoteknikermotei Kobenhavn1920,
Copenhagen, p. 49. Reprinted in: Elektroteknikeren
18, 1923, p. 99.
Scand J Statist 7
Application du calcul des probabilites en t6l6phonie.
Annales des postes, Telegraphes et Teliphones 14,
1925, p. 617.
1925 Et bevis for Maxwells Lov, Hovedsetningen i den
kinetiske Luftteori. Fysisk Tidsskr. 23, p. 40.
Demonstrations de la loi de Maxwell, proposition
fondamentale de la theorie des gaz. La Vie Technique
et Industrielle 8, 1926, p. 72.
1926 Some applications of the method of statistical
equilibrium in the theory of probabilities. Den
sjette skandinaviske Matematikerkongres i Kobenhavn 1925, Copenhagen, p. 157.
Quelques applications de la m6thode de l'equilibre
statistique dans la th6orie des probabilit6s. Annales
des Postes, Telegrapheset Telephones17, 1928, p. 743.
1929 Problem 15. Mat. Tidsskr. B: 36.
Secondary reading:
Brockmeyer, Halstr0m, H. L. & Jensen, A. (1948). The Life
and Works of A. K. Erlang. Trans.Dan. Acad. Techn.Sci.,
No. 2 (with complete bibliography and collected works
in English translation).
Gram, Jorgen Pedersen
1879 Om Rxkkeudviklinger,bestemt ved Mindste Kvadraters
Metode. K0benhavn.
German version: Ueber die Entwiklung reeller Functionen in Reihen mittelst der Methode der kleinsten
Quadrate. J. reine angew. Math., 1883, 94, 41-73.
Om Konstruktion af Normaltilvekster med saerligt
Hensyn til Iakttagelserne fra Oddsherred. (On the
construction of standard growth with special
emphasis on observations from Oddsherred.) Tidsskr.
Skovbrug 3, 207-70.
1883 Om kvadratur af Fejlkurver. (On the quadrature of
frequency curves.) Tidsskr. Math. (5) 1, 65-72.
1884 Om udjevning av Dodelighedsiagttagelser og Oppermann's Dodelighedsformel. (On smoothing mortality
curves and the mortality formula of Oppermann.)
Tidsskr. Math. (5) 2, 113-39.
1889 Om Middelfejl paa Vxrdien af Livsforsikringer. (On
mean errors of the capital value in life insurance.)
Tidsskr. Math. (5) 5, 97-120.
Tillkg til Afhandlingen om Middelfejl paa Vwerdienaf
Livsforsikringer. (Appendix to the paper "On mean
errors of the capital value in life insurance".) Tidsskr.
Math. (5) 5, 184-7.
Om Konstruktion af Normaltilvakster med saerligt
Hensyn til Iagttagelserne fra Oddsherred. (On the
construction of standard growth with special emphasis
on observations from Oddsherred). Tidsskr. Skovbrug 11, 97-151.
1900 La science actuarielle en Danemark. 3. International
Congress of Actuaries.
1904 Om Makehams Dodelighedsformel og dens Anvendelse ph ikke normale Liv. (On the mortality formula
of Makeham and its application to non normal lives.)
Aktuaren. (This journal appeared in one volume
only, Copenhagen.)
1909 Ober die Sicherheitsreserven der Lebensversicherung.
6. International Congress of Actuaries.
Secondary reading:
Nielsen, N. (1916): Dr. J. P. Gram. Nyt Tidsskr. Math.
A: 27, 48-53.
Early Scandinavian statistics
127
1906 Rapport sur la statistique de la fecondite du mariage.
Bull. Inst. Int. Stat. 15, no. 2, 398-401.
1908 Fecondite du mariage. Nombre des enfants par famille.
1869 Bibliographiestatistique du Royaume de Norvege pour
Bull. Inst. Int. Stat. 17, no. 2, 169-75.
les annees 1850-1869, Christiania, 9 pp.
1911 Documents concernant la statistique de la population
FolkemaengdensBeva?gelsei Aarene 1856-1865. (Popudes pays sans recensement. Rapport. Bull. Inst. Int.
lation movements in the years 1856-1865.) Chr.,
Stat. 19, no. 1, 142-56.
Departementet for det Indre, C. no. 1, s. III-LXXV.
Documents concernant la statistique internationale de
Rapport au Congres international de statistique a la
la repartition des revenus prives. Rapport. Bull.
Haye sur l'etat de la statistique officielle du Royaume
Inst. Int. Stat. 19, no. 2, 102-98.
de Norvege. Chr., 8 pp.
1912 Bevolkerungsstatistik der Lander ohne Volkzahlung.
1871 Om D0deligheden i det f0rste Leveaar. (On the morGeogr. Zeitschr. 18, 214-19.
tality in the first year of living.) Christiania Vid.
1915 Eilert Sundts befolkningsstatistiske lov. (The demoForh., 438-55.
graphical law of Eilert Sundt). Statsok. Tidsskr. 29.
1873 Nogle Oplysninger om Forholdet mellem AEgteskaber
La r6partition des revenues et fortunes prives. Rapport.
og F0dsler med saerligt Hensyn til AEgteskabernes
Bull. Inst. Int. Stat. 20, no. 2, 619-48.
stiftelsestid. (Some information on the relation be1918 The history and development of statistics in Norway.
tween marriges and births with special regard to
The history of statistics (ed. J. Koren). New York.
the time of establishment of the marriages). Christia1919 An attempt at a statistical determination of the birth
nia Vid. Forh.
rate in the United States. Quarterlypub. Amer. Stat.
1878 F&ondit6 des mariages en Norvege calcul6e a l'aide de
Ass. 16, 442-57.
donnees sur les naissance legitime reparties par
ann6es de mariage des parents. Cong. Int. Demogr.,
Secondary reading:
Paris, 4, 221-3.
1882 Bidrag til en norsk Befolkningsstatistikk. Innledning Rygg, N. (1919). Direkt0r A. N. Kier: Mindeord i Stats0konomisk forenings m0te, 28. apr. 1919. Statsok. Tidsskr.
til Tabeller indeholdende Resultaterne af Folke1-6.
teellingen i Norge i Januar 1876. (Contributions to
a Norwegian population statistics.) Det statistiske Seng, Y. P. (1951). Historical survey of the development
of sampling theories and practice. Jour. Roy. Stat. Soc.,
Centralbureau. Norges off. Stat., n.R.C., 1.
pp. 214-31. Reprinted in Kendall & Plackett (ed.) (1977):
Sekreter J. N. Mohns statistiske Virksomhet. (The
Studies in the History of Statistics and Probability, vol. 2,
statistical works of secretary J. N. Mohn.) MedLondon.
delelser fra Det Statistiske Centralbureau,1, 57-61.
1885 Fecondite'du mariage. Christiania. 10 pp.
Westergaard, H. (1919). Anders Nicolai Kihr. Statsok.
Tidsskr.
Frugtbarhedsforholdene i )Egteskabet. (Fertility in
the marriage.) Meddelelser Stat. Centr. 4, 136-8.
1888 Livs og D0dstabeller for det norske Folk etter Erfaringer fra Tiaaret 1871/72-1880/81. (Life and
Lindeberg, Jarl Waldemar
death tables for the Norwegian people.) Norges off.
1920 Ober das Exponentialgesetz in der WahrscheinlichStat., R. 3, 68.
keitsrechnung. Ann. Ac. Sc. Fenn. (A)XVI, no. 1,
1893-94 Intaegts og formuesforhold i Norge. (Income and
1-23.
fortune relations in Norway). Statsok. tidsskr.
1922 Eine neue Herleitung des Exponentialgesetzes in der
(Suppl.), 150 pp.
Wahrscheinlichkeitsrechnung. Math. Zeitschr. 15.
1894 Untersuchungen iuber die Einkommens- und VerUber das Gauss'sche Fehlergesetz. Skand. Aktuariemogensverhiiltnissein Norwegen. Der Arbeiterfreund
tidsskr. 5.
32, 455-79.
1895 Observations et experiences concernant des d6nombre- 1924 13ber die Berechnung des Mittelfehlers des Resultates
einer Linientaxierung. Acta Forest. Fenn. 25: 5.
ments representatifs. Bull. Inst. Inst. Stat. 9, no. 2,
1925 Ober die Begriffe Schiefheit und Excess in der
176-83.
mathematischen Statistik. Skand. Aktuarietidsskr.8.
1897 Den reprxsentative unders0gelsesmethode. (The retber die Korrelation. 6. Skand. Matem. Kongr. Kobenpresentativemethod of statistical surveys.) Christiania
havn.
Vid. Skr., Historisk-filosofisk klasse 2, no. 4, 34 p.
Reprinted at the Centenary of the Central Bureau 1926 Zur Theorie der Linientaxierung. Acta Forest. Fenn.
31: 6.
of Statistics, with English translation and complete
1929 Some remarks on the mean error of the percentage of
bibliography: Kier, A. N.: Den representative
correlation. Nord. Statist. Tidsskr. 8.
Unders0gelsesmethode. Samfunnsokonomiske StuZur Korrelationstheorie. Ann. ASF. A: 32: 1. (Comm.
dier, Statistisk Sentralbyrd,no. 27.
in honorem E. L. Lindelof.)
1899 Die reprasentative Untersuchungsmethode. All. Stat.
1931 Uiberdie Herleitung einiger Formeln fur mittlere Fehler.
Arch. 5, 1-22.
Sur la m6thodes representatives out typologiques
Skand. Aktuarietidsskr. 14.
appliqu6es it la statistique. Bull. Inst. Inst. Stat. 11,
no. 1, 180-9.
1903 Observations concernant le recensement des populaLundberg, Ernst Filip Oskar
tions non 6num&r6es. Theses se rattachant au
1903 Approximeradframstdllning av sannolikhetsfunktionen.
"Draft by Mr. Baines: On the census of unenume4terfdrsdkring av kollektivrisker. (Approximations
rated populations". Bull. Int. Inst. Stat. 13, no. 1,
to the probability function. Reinsurance of collective
56-8.
risks.) Uppsala.
Recensement de la population de la Chine. Formulaires
1909 Zur Theorie der Ruickeversicherung.Trans.Int. Congr.
et instructions. Meddelelser Stat. Cent. 21, Suppl.
Act. Vienne.
1903-05 Statistische Beitrage zur Beleuchtung der ehelichen
1919 Teorin for riskmassor. (The theory of risk masses.)
Fruchtbarkeit. Christiania Vid. Skr. Historisk-filosoFtrsdkringsinspektionenspubl. Stockholm.
fisk klasse.
Kixr, Anders Nicolai
Scand J Statist 7
128
T. Schweder
1926-28 Fdrsakringsteknisk riskutjdmning, L Teori. (Insurance technical risk smoothing.) Stockholm.
1930 tCber die Wahrscheinlichkeitsfunktion einer Risikenmasse. Skand. Akt. Tidsskr.
1934 On the numerical application of the collective risk
theory. De Fdrenade Jubilee Volume. Stockholm.
Secondary reading:
Cram6r, H. (1969). Historical review of Filip Lundberg's
work on risk theory. Skand. Akt. Tidsskr., no. 3-4
Suppl.
Grenholm, A. & Cramer, H. (1969). Filip Lundberg, Fdrgrundsman i svensk livsfdrsdkring.Stockholm.
1859
1862
1863
Oppermann, Ludvig Henrik Ferdinand
1857 Bidrag til Landmaalingens Theori. (Contributions to
the theory of geodesy.) Tidsskr. Krigsvaxsen,33244.
1863 Under the signature "En Dilettant": En Foresp0rgsel.
(A request.) Tidsskr. Math. (1) 5, p. 16.
Under the signature "En Dilettant": Minimumsproblemer. (Minimum problems.) Tidsskr. Math. (1)
5, 17-26.
1866 Om Livsforsikringer og Livrenter. (On life insurance
and pensions.) Copenhagen, 24 pp.
1869 Notes on Newton's formulae for interpolation. The
Assurance Mag. 15, 145-8 and 177-9.
1870 On Brigg's formula for interpolation. The Assurance
Mag. 15, 312.
On the graduation of life tables, with special application to the rate of mortality in infancy and childhood. The Assurance Rec., Febr. 11.
1871 Om Kvadratur. (On quadrature.) Tidsskr. Math. (3) 1
11-27.
1872 Elementaere Darstellung, der numerischen Summation
und Quadratur.Copenhagen, 21 pp.
Zur Begriindungder allgemeinenFehlertheorie(Methode
der kleinsten Quadraten). Hamburg, 20 pp.
Secondary reading:
Gram, J. P. (1883). Ludvig Henrik Ferdinand Oppermann.
Tidsskr. Math. (5) 1, 137-44.
Gram, J. P. (1884). Om udjevning av Dodelighedsiagttagelser og Oppermann's D0delighedsformel. (On smoothing mortality curves and the mortality formula of Oppermann.) Tidsskr. Math. (5) 2, 113-39.
Sebelien, J. (1883. En grafisk Fremstelling av Forsogsrakker. (A graphical representation of observations.)
Tidsskr. Math. (5) 1, 186-90.
Thiele, T. N. (1890). Et stykke arvegods fra professor Oppermann. Nyt Tidsskr. Mat. 1.
Sundt, Eilert
1850 Beretning om fante- eller Landstrygerfolket i Norge.
(Account of the gypsy people in Norway.) Christiania. New ed. Oslo, 1974.
1855 Om Dodeligheden i Norge. (On mortality in Norway.)
Chr. New ed. Oslo, 1975.
Om Giftemaal i Norge. (On marriage in Norway.) Chr.
New ed. Oslo, 1975.
1857 Om Swdeligheds-Tilstandeni Norge. (On the state of
morality in Norway.) Chr. New ed. Oslo, 1976.
1858 Om Roros og omegn. (On Roros and the surrounding
district.) Chr. New ed. Oslo, 1975.
Om Piperviken og Ruselokbakken. Undersogelse om
arbeiderklassens kaar og sxder i Christiania. (On
Scand J Statist 7
1864
1865
1868
Piperviken and Rusel0kbakken. Investigations of
the conditions and morality of the working class in
Christiania.) Chr. New ed. Oslo, 1975.
Fortsat Beretning om Fantefolket. (Continued account
of the gypsy people.) Chr. New ed. Oslo, 1974.
Om Edrueligheds-Tilstandeni Norge. (On temperance
conditions in Norway.) Chr. New ed. Oslo, 1976.
Harham. Et Exempelfra Fiskeri-Distrikterne.(Harham.,
An example from the fishery districts.) Chr. New
ed. Oslo, 1975.
Anden Aars-Beretning om Fantefolket. (Second annual
account of the gypsy people.) Chr. New ed. Oslo,
1974.
Tredie Aars-Beretning om Fantefolket. (Third annual
account of the gypsy people.) Chr. New ed. Oslo,
1974.
Fortsat Bidrag angaaende Sxdeligheds-Tilstanden I
Norge. (Continued contribution to the state of
morality in Norway.) Chr. New ed. Oslo, 1976.
Fjerde Aars-Beretning om Fantefolket. (Fourth annual
account of the gypsy people.) Chr. New ed. Oslo,
1974.
Tredie Beretning om Sxedeligheds-Tilstandeni Norge.
(On the state of morality in Norway, third account.'
Chr. New ed. Oslo, 1976.
Secondary reading:
Allwood, M. S. (1957). Eilert Sundt. A pioneer in sociology
and social anthropology. Oslo.
Arctander, S. (1952). Sosialstatistikkens historie gjennom 100
dr (1850-1950). Oslo, SSB, NOS XI 113.
Christie, N. (1958). Eilert Sundt som fanteforsker og sosialstatistiker. Institutettet for sosiologi. Universitetet i Oslo.
Mimeographed.
Christophersen, H. 0. (1962). Eilert Sundt. En dikter i kjennsgjerninger. Oslo.
Lunde, H. (1917). Eilert Sundt som folkelerer. Kristiania.
Otnes, P. (1977). Den skjulte sosiologien. Forlopere for
sosiologi og lignende samfunnsvitenskap.1848-1949. Instituttet for sosiologi. Universitetet i Oslo, Arbeidsnotater
Nr. 86.
Rygg, N. (1917). Eilert Sundt 1817 - 8. aug. - 1917. Statsxk.
Tidsskr. Kristiania. Reprinted in Nord. Stat. Tidsskr. 8,
1929.
Thiele, Thorvald Nicolai
1871 En matematisk Formel for Dddeligheden,prdvet paa en
av Livsforsikringsanstalten af 1871 benyttet Erfaringsrxkke. (A mathematical mortality formula,
...) Copenhagen.
1880 Sur la compensation de quelques erreurs quasi-systi.matiquespar la methode de moindres carres. Copenhagen, 29 pp.
Om Anvendelse af Mindste Kvadraters Metode i nogle
Tilfelde, kvor en Komplikation af visse Slags uensartede tilfxldige Fejlkilder giver Fejlene en "systematisk Karakter". (On the application of the method
of least squares in situations where irregular random
errors make the errors have a "systematical charac..
ter".) Copenhagen, 28 pp.
1889 Forelaxsningerover Almindelig Iagttagelseslere: Sann..
synlighedsregning of mindste Kvadraters Metode.
(Lectures on the general theory of observations:
Calculus of probability and the method of least;
squares.) Copenhagen, 117 pp.
1890 Et stykke Arvegods fra professor Oppermann. (A piece
of inheritance from professor Oppermann.) Nyt
Tidsskr. Mat. 1.
statistics 129
EarlyScandinavian
1892 Iagttagelsestheoretiske Regninger angaaende Julius
Thomsens Varmefylde og Vegtfylde Bestemmelser.
(Statistical computations related to the observations
on heat and weight of Julius Thomsen.) Vid. Selsk.
Forh., 70 pp.
1897 Elementar Iagttagelseslaxre. (Elementary theory of
observations.) Copenhagen, 128 pp.
1899 Om Iagttagelseslhrens Halvinvarianter. (On the half
invariants in the theory of observations.) Vid. Selsk.
Forh., 7 pp.
1903 Theory of observations. London, 143 pp.
1906 Et Arvelighedssp0rgsmaal belyst ved Iagttagelseslere.
(A problem of genetics studied by the theory of observations.) Vid selsk. Forh., 4 pp.
1909 Interpolationsrechnung.Leipzig, 12+ 175 pp.
Secondary reading:
Burrau, C. T. (1929). T. N. Thiele 1838-1910. Nord. stat.
tid. 8, 340-8.
Gram, J. P. (1910). Thiele som Aktuar. Dansk Forsikrings
Aarbog.
Gram, J. P. (1910). Thorvald Nicolai Thiele. Nyt Tidsskr.
Mat. (A) 21, 73-8.
Wargentin,Pehr Wilhelm
In "Kungliga Vetenskaps Akademiens Handlingar" (Proceedings of the Royal Academy of Science), Stockholm:
1754-55 Six papers under the heading:
Anmarkningar om nyttan af arliga Forteckningar pa
fodda och doda i ett land. (Remarks on the value
of yearly records of births and deaths in a country.)
1766 Mortaliteten i Sverige, i anledning Tabellverket.
Mortality in Sweden, Stockholm, 1930.
9 - 801928
1767 Uti hvilka MAnaderflere Maniskor Arligenfddas och
do i Sverige. (In what months more people are born
or die in Sweden.)
1769 Om Stockholms Stads tilvaxt i Folkrikhet ifran Ar
1721, til och med 1766. (On the population growth
in Stockholm from 1721 to 1766.)
1782 Folkemangden uti hele Riket och uti hvart Hdfdingedome, tillika med HushAllens antal i Staderna och
pi Landet, sAdantsom de af Tabell-verket befunnits
Aren 1751 och 1772, med korta anmarkningar.
(Population size in the Kingdom and in the counties,
1751 and 1772.)
Some more papers are reprinted in:
Hjelt (1899). De forsta officiella relationerna om svenska
tabellverket (1749-1759). Fennia XVI.
Hjelt (1900). Det svenska tabellverkets uppkomst, organisation och tidligare verksamhet. Fennia XVI.
Arosenius, E. (1928). Bidrag til det svenska Tabellverkets
historia. Stockholm.
Secondary literature:
Nordenmark, N. V. E. (1929. Pehr Wilhelm Wargentin
1717-1783. Nord. Stat. Tidsskr. 8.
Nordenmark, N. V. E. (1939). Pehr Wilhelm Wargentin.
Uppsala. (With a summary in French.)
Westergaard, H. (1932). Contributions to the History of
Statistics. London 1932. (Relevant chapters also printed
in: Kendall, M. & Plackett, R. L. (ed.) (1977): Studies in
the History of Statistics and Probability, vol. 2, London.)
Tore Schweder
Institute of Mathematical and Physical Sciences
University of Troms0
N-9001 Troms0
Norway
Scand J Statist 7