Maurice Tweedie

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Maurice Charles Kenneth Tweedie, British medical physicist and statistician from the University of Liverpool, was born in Reading, England September 30, 1919 and died March 14, 1996.[1][2] He 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, but his primary interest was in mathematical statistics where his accomplishments far surpassed his academic postings. This included pioneering work with the inverse Gaussian distribution.[3][4] Arguably his major achievement rests with the definition of a family of exponential dispersion models characterized by closure under additive and reproductive convolution as well as under transformations of scale that are now known as the Tweedie exponential dispersion models.[1][5] As a consequence of these properties the Tweedie exponential dispersion models are characterized by a power law 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.[6] The range of application of the Tweedie distributions is wide and includes:

References[edit]

  1. ^ a b Tweedie, M.C.K. (1984). "An index which distinguishes between some important exponential families". In Ghosh, J.K.; Roy, J. Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference. Calcutta: Indian Statistical Institute. pp. 579–604. MR 786162. 
  2. ^ Smith, C.A.B. (1997). "Obituary: Maurice Charles Kenneth Tweedie, 1919-96". Journal of the Royal Statistical Society, Series A 160 (1): 151–154. doi:10.1111/1467-985X.00052. 
  3. ^ Tweedie MCK (1957) Statistical properties of inverse Gaussian distributions. I. Ann Math Stat 28, 362–377
  4. ^ Tweedie MCK (1957) Statistical properties of inverse Gaussian distributions. II. Ann Math Stat 28, 695–705
  5. ^ Jørgensen, B (1987). "Exponential dispersion models". Journal of the Royal Statistical Society, Series B 49 (2): 127–162. 
  6. ^ Jørgensen, B; Martinez, JR & Tsao, M (1994). "Asymptotic behaviour of the variance function". Scand J Statist 21: 223–243. 
  7. ^ Kendal WS (2004) Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models. Ecol Complex 1, 193–209
  8. ^ a b c d Kendal WS & Jørgensen BR (2011) Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality. Phys. Rev E 84, 066120
  9. ^ Kendal WS & Jørgensen B (2011) Taylor's power law and fluctuation scaling explained by a central-limit-like convergence. Phys. Rev. E 83,066115
  10. ^ Kendal WS. 2002. A frequency distribution for the number of hematogenous organ metastases. Invasion Metastasis 1: 126--135.
  11. ^ Kendal WS (2003) An exponential dispersion model for the distribution of human single nucleotide polymorphisms. Mol Biol Evol 20 579-590
  12. ^ Kendal, WS (2004). "A scale invariant clustering of genes on human chromosome 7". BMC Evol Biol 4: 3. doi:10.1186/1471-2148-4-3. PMC 373443. PMID 15040817. 
  13. ^ Kendal WS (2001) A stochastic model for the self-similar heterogeneity of regional organ blood flow. Proc Natl Acad Sci U S A 98, 837-841