Maurice Charles Kenneth Tweedie (born September 30, 1919 – died March 14, 1996), or Kenneth Tweedie, was a British medical physicist and statistician from the
University of Liverpool
, mottoeng = These days of peace foster learning
, established = 1881 – University College Liverpool1884 – affiliated to the federal Victoria Universityhttp://www.legislation.gov.uk/ukla/2004/4 University of Manchester Act 200 ...
. He was known for research into the
exponential family probability distributions.
Education and career
Tweedie read physics at the
University of Reading and attained a B.Sc. (general) and B.Sc. (special) in physics in 1939 followed by a M.Sc. in physics 1941. He found a career in
radiation physics
Health physics, also referred to as the science of radiation protection, is the profession devoted to protecting people and their environment from potential radiation hazards, while making it possible to enjoy the beneficial uses of radiation. He ...
, but his primary interest was in
mathematical statistics where his accomplishments far surpassed his academic postings.
Contributions
Tweedie distributions
Tweedie's contributions included pioneering work with the
Inverse Gaussian distribution.
Arguably his major achievement rests with the definition of a family of
exponential dispersion models 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 ( and ) that produces a third function (f*g) that expresses how the shape of one is ...
as well as under
transformations of scale that are now known as the
Tweedie exponential dispersion models.
As a consequence of these properties the Tweedie exponential dispersion models are characterized by 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 proportional relative change in the other quantity, inde ...
relationship between the variance and the mean which leads them to become the foci of
convergence for a
central limit like effect that acts on a wide variety of random data. The range of application of the Tweedie distributions is wide and includes:
*
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 propos ...
,
*fluctuation scaling,
*
1/''f'' noise,
*
random matrix theory,
*hematogenous cancer
metastasis
Metastasis is a pathogenic agent's spread from an initial or primary site to a different or secondary site within the host's body; the term is typically used when referring to metastasis by a cancerous tumor. The newly pathological sites, then, ...
,
[Kendal WS. 2002. A frequency distribution for the number of hematogenous organ metastases. Invasion Metastasis 1: 126–135.]
*genomic structure and
evolution
Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
,
*regional blood flow heterogeneity,
*
multifractality.
*
self-organized criticality[
]
Tweedie's Formula
An additional area of Tweedie's work was the development of a formula which Efron (2011) described as offering "a simple empirical Bayes approach to correcting selection bias".
References
{{reflist
People from Reading, Berkshire
Alumni of the University of Reading
Medical physicists
1919 births
1996 deaths
Academics of the University of Manchester
Academics of the University of Liverpool
British statisticians