Jarl Waldemar Lindeberg
Encyclopedia
Jarl Waldemar Lindeberg was a Finnish
mathematician
known for work on the central limit theorem
.
Lindeberg was son of a teacher at the Helsinki Polytechnical Institute
and at any age showed mathematical talent and interest. The family was well off and later Jarl Waldemar would prefer to be a reader than a full professor. Lindeberg's career centred on the University of Helsinki
. His early interests were in partial differential equation
s and the calculus of variations
but from 1920 he worked in probability
and statistics
. In 1920 he published his first paper on the central limit theorem
. His result was similar to that obtained earlier by Lyapunov
whose work he did not then know. However, their approaches were quite different; Lindeberg's was based on a convolution
argument while Lyapunov used the characteristic function
. Two years later Lindeberg used his method to obtain a stronger result: the so-called Lindeberg condition. His work on probability led to him becoming involved in applied fields. He developed what we know as Kendall's tau and he found the two first moments of its sampling distribution. Lindeberg used line transect methods in forestry
, and when in 1926 determining the necessary number of transects to obtain a sufficiently precise confidence interval
, he seems to have rediscovered Student's t-distribution.
The Swedish mathematician Harald Cramér
met Lindeberg in 1922. He later recalled this story about Lindeberg and the beautiful farm he owned. "When he was reproached for not being sufficiently active in his scientific work, he said 'Well, I am really a farmer.' And if somebody happened to say that his farm was not properly cultivated, his answer was 'Of course my real job is to be a professor.' I was very fond of him and saw him often during the following years."
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for work on the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
.
Lindeberg was son of a teacher at the Helsinki Polytechnical Institute
Helsinki University of Technology
Aalto University School of Science and Technology , was the temporary name for Helsinki University of Technology during the process of forming the Aalto University...
and at any age showed mathematical talent and interest. The family was well off and later Jarl Waldemar would prefer to be a reader than a full professor. Lindeberg's career centred on the University of Helsinki
University of Helsinki
The University of Helsinki is a university located in Helsinki, Finland since 1829, but was founded in the city of Turku in 1640 as The Royal Academy of Turku, at that time part of the Swedish Empire. It is the oldest and largest university in Finland with the widest range of disciplines available...
. His early interests were in partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s and the calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
but from 1920 he worked in probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
. In 1920 he published his first paper on the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
. His result was similar to that obtained earlier by Lyapunov
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov was a Russian mathematician, mechanician and physicist. His surname is sometimes romanized as Ljapunov, Liapunov or Ljapunow....
whose work he did not then know. However, their approaches were quite different; Lindeberg's was based on a convolution
Convolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...
argument while Lyapunov used the characteristic function
Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any random variable completely defines its probability distribution. Thus it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative...
. Two years later Lindeberg used his method to obtain a stronger result: the so-called Lindeberg condition. His work on probability led to him becoming involved in applied fields. He developed what we know as Kendall's tau and he found the two first moments of its sampling distribution. Lindeberg used line transect methods in forestry
Forestry
Forestry is the interdisciplinary profession embracing the science, art, and craft of creating, managing, using, and conserving forests and associated resources in a sustainable manner to meet desired goals, needs, and values for human benefit. Forestry is practiced in plantations and natural stands...
, and when in 1926 determining the necessary number of transects to obtain a sufficiently precise confidence interval
Confidence interval
In statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
, he seems to have rediscovered Student's t-distribution.
The Swedish mathematician Harald Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
met Lindeberg in 1922. He later recalled this story about Lindeberg and the beautiful farm he owned. "When he was reproached for not being sufficiently active in his scientific work, he said 'Well, I am really a farmer.' And if somebody happened to say that his farm was not properly cultivated, his answer was 'Of course my real job is to be a professor.' I was very fond of him and saw him often during the following years."
Writing available on the web
- J. W. Lindeberg, Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung, Mathematische Zeitschrift, 15 (1922) 211-225.
Commentary
- L. Le Cam (1986) The Central Limit Theorem Around 1935, Statistical Science, Vol. 1, No. 1. (Feb), pp. 78-91.
- Gustav ElfvingGustav ElfvingGustav Elfving was a Finnish mathematician and statistician. In statistics, he wrote pioneering papers about the optimal design of experiments...
(1981) The History of Mathematics in Finland 1828-1918. Societas Scientarium Fennica, Helsinki.
Biography
- G. Elfving (2001) Jarl Waldemar Lindeberg, Statisticians of the Centuries (ed. C. C. Heyde and E. Seneta) pp. 318-321. New York: Springer.
- Harald Cramér (1976) Half a Century with Probability Theory: Some Personal Recollections, Annals of Probability, Vol. 4, No. 4. (Aug.), pp. 509-546.
