Bent Jørgensen (15 April 1954 – 19 November 2015) was a Danish statistician from the

University of Southern Denmark The University of Southern Denmark (, SDU) has campuses located in Southern Denmark and on Zealand. It offers a number of joint programmes in co-operation with the University of Flensburg and the University of Kiel. Contacts with regional indu ...

whose research was focused on two related topics in statistics: dispersion models and the analysis of non-normal correlated data.

Education and career

Jørgensen studied statistics and was conferred a Cand. Scient. degree in 1979 from

Aarhus University Aarhus University (, abbreviated AU) is a public research university. Its main campus is located in Aarhus, Denmark. It is the second largest and second oldest university in Denmark. The university is part of the Coimbra Group, the Guild, and Ut ...

followed by a Ph.D. in 1987 (

Odense University Odense University was a university in Odense, Denmark. It was established in 1966. In 1998, the university was merged with two other institutions to form the University of Southern Denmark. Its campus is now known as University of Southern Denmar ...

) and Dr. Scient. in 1997 (

Aalborg University Aalborg University (AAU) is an international public university with campuses in Aalborg, Esbjerg, and Copenhagen, Denmark. Founded in 1974, the university awards bachelor's degrees, master's degrees, and PhD degrees in a wide variety of subje ...

). In 1987 he joined the Instituto de Matemática Pura e Aplicada at

Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by population, second-most-populous city in Brazil (after São Paulo) and the Largest cities in the America ...

, and from 1992 to 1997 he was affiliated with the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

in Canada. His subsequent appointments were with

and the

Research

Jørgensen identified a number of other classes of dispersion models which included the multivariate dispersion models, the dispersion models for extremes and the dispersion models for geometric sums. Dispersion models serve as error distributions for

generalized linear models In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by ...

and represent a broad class of distributions that allow for the analysis of data that go beyond the restrictions of the

normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...

. These models include both the proper dispersion models and the exponential dispersion models. He had an interest in a class of exponential dispersion models identified by Maurice Tweedie characterized by closure under additive and reproductive

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

as well as under transformations of scale that are now called the

Tweedie distributions In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the cl ...

. These models express a

power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the ...

relationship between the variance and the mean which manifests in ecological systems where it is known as

Taylor's law Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first propose ...

and in physical systems where it is known as ''fluctuation scaling''. Jørgensen proved a number of convergence theorems, related to the

central limit theorem In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distributi ...

, that specified the asymptotic behavior of the variance functions of the Tweedie models. These theorems would indicate that certain types of Tweedie models should have a role as equilibrium distributions in natural systems. They can be used to explain the origin of

as well as 1/''f'' noise and multifractality. Consequent to Jørgensen's work the Tweedie distributions and their convergence theorem have provided mechanistic insight into complicated natural systems that manifest features of

self-organized criticality Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phas ...

and random fractals.

Selected works

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References

{{DEFAULTSORT:Jorgensen, Bent 1954 births 2015 deaths Danish statisticians Aarhus University alumni University of Southern Denmark alumni Academic staff of the University of Southern Denmark Aalborg University alumni Academic staff of the University of British Columbia Instituto Nacional de Matemática Pura e Aplicada researchers 20th-century Danish mathematicians Mathematical statisticians