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. 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. 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. 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. The range of application of the Tweedie distributions is wide and includes:
- Taylor's law,
- fluctuation scaling,
- 1/f noise,
- random matrix theory,
- hematogenous cancer metastasis,
- genomic structure and evolution,
- regional blood flow heterogeneity,
- self-organized criticality
- 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.
- 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
- 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 Statist 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
- 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
- Kendal WS & Jørgensen B (2011) Taylor's power law and fluctuation scaling explained by a central-limit-like convergence. Phys. Rev. E 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
- 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, 837–841
- Kendal, W. (2015). "Self-organized criticality attributed to a central limit-like convergence effect". Physica A 421: 141–150.