Data: 19/03/2009, 16h Local: sala 311, Departamento de Ciências Exatas, ESALQ/USP Titulo: The Power Laws of Taylor and Tweedie Conferencista: Bent Jørgensen (University of Southern Denmark) Resumo: Taylor's power law, which has been observed empirically in many different biological, physical and social systems, says that the variance is proportional to a power of the mean. L.R. Taylor first used this relationship in 1961 to describe the spatial clustering of animals and plants within their habitats. Over time the power law has been observed for clustering phenomena in areas such as ecology, epidemiology, genetics and physics, and Taylor's name is now associated with the power law in many applied areas. The explanations for such clustering phenomena have, however, been as disparate as their many manifestations. In statistics the interest in power laws dates back a long time, but in 1984 M.C.K. Tweedie proposed a natural exponential family type of distribution with power variance structure, thereby presenting a specific distributional form to explain the power law. Soon after, it emerged that Tweedie distributions appear as limiting laws in a kind of central limit theorem, thereby offering, for the first time, a plausible explanation for the ubiquity of the power variance law in nature. We present a survey of these developments, and discuss some of their implications for statistical modelling. -- Clarice Garcia Borges Demétrio Departamento de Ciências Exatas Escola Superior de Agricultura "Luiz de Queiroz" Universidade de São Paulo, 13418-900 Piracicaba, SP Brasil phone: 55 19 34294144 R216 Biometry, the active pursuit of biological knowledge by quantitative methods.? ? R.A. Fisher, 1948 -- Clarice Garcia Borges Demétrio Departamento de Ciências Exatas Escola Superior de Agricultura "Luiz de Queiroz" Universidade de São Paulo, 13418-900 Piracicaba, SP Brasil phone: 55 19 34294144 R216 Biometry, the active pursuit of biological knowledge by quantitative methods.? ? R.A. Fisher, 1948
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Um novo titulo e resume. Bent The Power Laws of Taylor and Tweedie Conferencista: Bent Jørgensen, University of Southern Denmark Taylor's power law, which has been observed
empirically in many different biological, physical and social systems, says
that the variance is proportional to a power of the mean. L.R. Taylor first
used this relationship in 1961 to describe the spatial clustering of animals
and plants within their habitats. Over time the power law has been observed for
clustering phenomena in areas such as ecology, epidemiology, genetics and
physics, and Taylor's name is now associated with the power law in many applied
areas. The explanations for such clustering phenomena have, however, been as
disparate as their many manifestations. In statistics the interest in power
laws dates back a long time, but in 1984 M.C.K. Tweedie proposed a natural
exponential family type of distribution with power variance structure, thereby
presenting a specific distributional form to explain the power law. Soon after,
it emerged that Tweedie distributions appear as limiting laws in a kind of
central limit theorem, thereby offering, for the first time, a plausible
explanation for the ubiquity of the power variance law in nature. We present a
survey of these developments, and discuss some of their implications for
statistical modelling. |