Jarl Waldemar Lindeberg (4 August 1876,

Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...

– 24 December 1932, Helsinki) was a

Finnish Finnish may refer to: * Something or someone from, or related to Finland * Culture of Finland * Finnish people or Finns, the primary ethnic group in Finland * Finnish language, the national language of the Finnish people * Finnish cuisine See also ...

mathematician known for work on the

central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselv ...

Life and work

Lindeberg was son of a teacher at the Helsinki Polytechnical Institute and at an early 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 The University of Helsinki ( fi, Helsingin yliopisto, sv, Helsingfors universitet, abbreviated UH) is a public research university located in Helsinki, Finland since 1829, but founded in the city of Turku (in Swedish ''Åbo'') in 1640 as the ...

. His early interests were in

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s and the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

but from 1920 he worked in

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

and

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

. In 1920 he published his first paper on the

. 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 In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...

argument while Lyapunov used the

characteristic function In mathematics, the term "characteristic function" can refer to any of several distinct concepts: * The indicator function of a subset, that is the function ::\mathbf_A\colon X \to \, :which for a given subset ''A'' of ''X'', has value 1 at points ...

. Two years later Lindeberg used his method to obtain a stronger result: the so-called ''

Lindeberg condition In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit theorem (CLT) to hold for a sequence of independent random variables. Unlike the classical CLT, wh ...

''. His work on probability led to him becoming involved in applied fields. He developed what we know as

Kendall's τ In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a n ...

and he found the first two moments of its sampling distribution. Lindeberg used

line transect method In statistics, more specifically in biostatistics, line-intercept sampling (LIS) is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a “transect A transect is a path along which one c ...

s in

forestry Forestry is the science and craft of creating, managing, planting, using, conserving and repairing forests, woodlands, and associated resources for human and environmental benefits. Forestry is practiced in plantations and natural stands. Th ...

, and when in 1926 determining the necessary number of transects to obtain a sufficiently precise

confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...

, he seems to have rediscovered

Student's t-distribution In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in sit ...

. The Swedish mathematician

Harald Cramér Harald Cramér (; 25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. John Kingman described him as "one of the giants of statist ...

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." Lindeberg's work was unknown to

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...

, who proved the central limit theorem in his dissertation in 1935.See Section 3 of

Writing available on the web

Commentary

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Biography

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References

External links

Photograph of Lindeberg
on th

page
Tore Schweder: Early Statistics in the Nordic Countries
* {{DEFAULTSORT:Lindeberg, Jarl Waldemar Finnish mathematicians Finnish statisticians 1876 births 1932 deaths Probability theorists Scientists from Helsinki