Maurice Tweedie
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:
- Taylor's law,[7][8]
- fluctuation scaling,[9]
- 1/f noise,[8]
- random matrix theory,[8]
- hematogenous cancer metastasis,[10]
- genomic structure and evolution,[11][12]
- regional blood flow heterogeneity,[13]
- multifractality.[8]
- self-organized criticality[14]
References
- ^ a b Tweedie, M.C.K. (1984). "An index which distinguishes between some important exponential families". In Ghosh, J.K.; Roy, J (eds.). Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference. Calcutta: Indian Statistical Institute. pp. 579–604. MR 0786162.
{{cite conference}}: Unknown parameter|booktitle=ignored (|book-title=suggested) (help) - ^ 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.
- ^ Tweedie, MCK (1957). "Statistical properties of inverse Gaussian distributions. I.". Ann Math Stat. 28: 362–377. doi:10.1214/aoms/1177706964.
- ^ Tweedie, MCK (1957). "Statistical properties of inverse Gaussian distributions. II". Ann Math Stat. 28: 695–705.
- ^ Jørgensen, B (1987). "Exponential dispersion models". Journal of the Royal Statistical Society, Series B. 49 (2): 127–162.
- ^ Jørgensen, B; Martinez, JR; Tsao, M (1994). "Asymptotic behaviour of the variance function". Scand J Stat. 21: 223–243.
- ^ Kendal, WS (2004). "Taylor's ecological power law as a consequence of scale invariant exponential dispersion models". Ecol Complex. 1: 193–209. doi:10.1016/j.ecocom.2004.05.001.
- ^ 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. doi:10.1103/physreve.84.066120. PMID 22304168.
- ^ Kendal, WS; Jørgensen, B (2011). "Taylor's power law and fluctuation scaling explained by a central-limit-like convergence". Phys. Rev. E. 83: 066115. doi:10.1103/physreve.83.066115.
- ^ Kendal WS. 2002. A frequency distribution for the number of hematogenous organ metastases. Invasion Metastasis 1: 126–135.
- ^ Kendal, WS (2003). "An exponential dispersion model for the distribution of human single nucleotide polymorphisms". Mol Biol Evol. 20: 579–590. doi:10.1093/molbev/msg057.
- ^ 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.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ 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. doi:10.1073/pnas.98.3.837. PMC 14670.
- ^ Kendal, W. (2015). "Self-organized criticality attributed to a central limit-like convergence effect". Physica A. 421: 141–150. doi:10.1016/j.physa.2014.11.035.