Maurice Tweedie
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. He was known for research into the exponential family probability distributions.[1][2]
Maurice Charles Kenneth Tweedie | |||||
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| Born | September 30, 1919 | ||||
| Died | March 14, 1996 (aged 76) | ||||
| Education | University of Reading | ||||
| Known for | Inverse Gaussian distribution Tweedie distributions | ||||
| Scientific career | |||||
| Institutions | Virginia Tech University of Manchester University of Liverpool | ||||
| Academic advisors | Paul White Boyd Harshbarger | ||||
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, 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.[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]
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".[15]
References
- 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.
- 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 (2): 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 (3): 193–209. doi:10.1016/j.ecocom.2004.05.001.
- Kendal, WS; Jørgensen, BR (2011). "Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality". Phys. Rev. E. 84 (6): 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 (6): 066115. doi:10.1103/physreve.83.066115. PMID 21797449.
- 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 (4): 579–590. doi:10.1093/molbev/msg057. PMID 12679541.
- 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.
- Kendal, WS (2001). "A stochastic model for the self-similar heterogeneity of regional organ blood flow". Proc Natl Acad Sci U S A. 98 (3): 837–841. doi:10.1073/pnas.98.3.837. PMC 14670. PMID 11158557.
- 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.
- Efron, B (2011). "Tweedie's Formula and Selection Bias". Journal of the American Statistical Association. 106 (496): 1602–1614. doi:10.1198/jasa.2011.tm11181. JSTOR 23239562. PMC 3325056. PMID 22505788.