Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

Article

Dunn, Peter K. and Smyth, Gordon K.. 2008. "Evaluation of Tweedie exponential dispersion model densities by Fourier inversion." Statistics and Computing. 18 (1), pp. 73-86. https://doi.org/10.1007/s11222-007-9039-6
Article Title

Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

ERA Journal ID861
Article CategoryArticle
AuthorsDunn, Peter K. (Author) and Smyth, Gordon K. (Author)
Journal TitleStatistics and Computing
Journal Citation18 (1), pp. 73-86
Number of Pages14
Year2008
Place of PublicationGermany
ISSN0960-3174
1573-1375
Digital Object Identifier (DOI)https://doi.org/10.1007/s11222-007-9039-6
Web Address (URL)http://springerlink.metapress.com/content/j0v757370742/?p=f1bfe0cecc6b4e33aa702fd2258f30de&pi=0
Abstract

The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V (μ) = μ^p for p not between (0, 1). These distributions do not generally have density functions that can be written in closed form. However, they have simple moment generating functions, so the densities can be evaluated numerically by Fourier inversion of the characteristic functions. This paper develops numerical methods to make this inversion fast and accurate. Acceleration techniques are used to handle oscillating integrands. A range of analytic results are used to ensure convergent computations and to reduce the complexity of the parameter space. The Fourier inversion method is compared to a series evaluation method and the two methods are found to be complementary in that they perform well in different regions of the parameter
space.

Keywordscompound Poisson distribution; generalized linear models; numerical integration; numerical acceleration; power variance function
ANZSRC Field of Research 2020490599. Statistics not elsewhere classified
490406. Lie groups, harmonic and Fourier analysis
461399. Theory of computation not elsewhere classified
Public Notes

Deposited in accordance with the copyright policy of the publisher.
The original publication is available at www.springerlink.com

Byline AffiliationsDepartment of Mathematics and Computing
Walter and Eliza Hall Institute of Medical Research, Australia
Permalink -

https://research.usq.edu.au/item/9y99q/evaluation-of-tweedie-exponential-dispersion-model-densities-by-fourier-inversion

Log in to edit

Download files

Accepted Version
Dunn_Smyth_Stats_and_Comp_v18n1.pdf
File access level: Anyone

  • 2508
    total views
  • 1023
    total downloads
  • 1
    views this month
  • 0
    downloads this month

Export as

Related outputs

The teaching and learning of tertiary mathematics
Oates, Greg, Coupland, Mary, Dunn, Peter, Evans, Tanya, Galligan, Galligan and Hernandez Martinez, Paul. 2024. "The teaching and learning of tertiary mathematics." Mesiti, Carmel, Seah, Wee Tiong, Kaur, Berinderjeet, Pearn, Cath, Jones, Anthony Jone, Cameron, Scott, Every, Emma and Copping, Kate (ed.) Research in Mathematics Education in Australasia 2020–2023. Singapore . Springer. pp. 187-211
Statistics poster competitions: an opportunity to connect academics and teachers
Dunn, Peter K., Richardson, Alice, Prodromou, Theodosia and Axelsen, Taryn. 2020. "Statistics poster competitions: an opportunity to connect academics and teachers." Statistics Education Research Journal. 19 (1).
Research into teaching and learning of tertiary mathematics and statistics
Galligan, Linda, Coupland, Mary, Dunn, Peter K., Hernandez Martinez, Paul and Oates, Greg. 2020. "Research into teaching and learning of tertiary mathematics and statistics." Way, Jennifer, Attard, Catherine, Anderson, Judy, Bobis, Janette, McMaster, Heather and Cartwright, Katherin (ed.) Research in mathematics education in Australasia 2016–2019. Singapore. Springer. pp. 269-292
Ten simple rules for learning the language of statistics
Richardson, Alice M., Dunn, Peter K., Carey, Michael D. and McDonald, Christine. 2016. "Ten simple rules for learning the language of statistics." MacGilivray, Helen, Martin, Michael A. and Phillips, Brian (ed.) OZCOTS 2016: Satellite to ASC 2016 Australian Statistical Conference. Canberra, Australia 08 - 09 Dec 2016 Australia.
Introductory statistics textbooks and the GAISE recommendations
Dunn, Peter K., Carey, Michael D., Farrar, Michael B., Richardson, Alice M. and McDonald, Christine. 2017. "Introductory statistics textbooks and the GAISE recommendations." The American Statistician. 71 (4), pp. 326-335. https://doi.org/10.1080/00031305.2016.1251972
Learning the language of statistics: challenges and teaching approaches
Dunn, Peter K., Carey, Michael D., Richardson, Alice M. and McDonald, Christine. 2016. "Learning the language of statistics: challenges and teaching approaches." Statistics Education Research Journal. 15 (1), pp. 8-27.
Instructor perceptions of using a mobile phone-based, free classroom response system in first-year statistics undergraduate courses: implications for teaching practice
Dunn, Peter K., Richardson, Alice, McDonald, Christine, Oprescu, Florin and Fairweather, Helen. 2011. "Instructor perceptions of using a mobile phone-based, free classroom response system in first-year statistics undergraduate courses: implications for teaching practice." Hannah, John and Thomas, Mike (ed.) 8th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics: Volcanic Delta 2011. Rotorua, New Zealand 27 Nov - 02 Dec 2011
Tertiary mathematics education
Coupland, Mary, Dunn, Peter K., Galligan, Linda, Oates, Greg and Trenholm, Sven. 2016. "Tertiary mathematics education." Maker, Katie, Dole, Shelley, Visnovska, Jana, Goos, Merrilyn, Bennison, Anne and Fry, Kym (ed.) Research in Mathematics Education in Australasia 2012-2015. Singapore. Springer. pp. 187-211
CRiSP: an instrument for assessing student perceptions of classroom response systems
Richardson, Alice M., Dunn, Peter K., McDonald, Christine and Oprescu, Florin. 2015. "CRiSP: an instrument for assessing student perceptions of classroom response systems." Journal of Science Education and Technology. 24 (4), pp. 432-447. https://doi.org/10.1007/s10956-014-9528-2
StatsCasts: screencasts for complementing lectures in statistics classes
Dunn, Peter K., McDonald, Christine and Loch, Birgit. 2015. "StatsCasts: screencasts for complementing lectures in statistics classes." International Journal of Mathematical Education in Science and Technology. 46 (4), pp. 521-532. https://doi.org/10.1080/0020739X.2014.990530
StatsCasts: supporting student learning of introductory statistics
McDonald, Christine, Dunn, Peter K., Loch, Birgit and Weiss, Vida. 2013. "StatsCasts: supporting student learning of introductory statistics." Deborah, King, Birgit, Loch and Leanne, Rylands (ed.) 9th Delta Conference of Teaching and Learning of Undergraduate Mathematics and Statistics 2013: Shining Through the Fog. Kiama, Australia 24 - 29 Nov 2013 Sydney, Australia.
Mobile-phone-based classroom response systems: students' perceptions of engagement and learning in a large undergraduate course
Dunn, Peter K., Richardson, Alice, Oprescu, Florin and McDonald, Christine. 2013. "Mobile-phone-based classroom response systems: students' perceptions of engagement and learning in a large undergraduate course." International Journal of Mathematical Education in Science and Technology. 44 (8), pp. 1160-1174. https://doi.org/10.1080/0020739X.2012.756548
Instructor perceptions of using a mobile-phone-based, free classroom response system in first-year statistics undergraduate courses
Dunn, Peter K., Richardson, Alice, McDonald, Christine and Oprescu, Florin. 2012. "Instructor perceptions of using a mobile-phone-based, free classroom response system in first-year statistics undergraduate courses." International Journal of Mathematical Education in Science and Technology. 43 (8), pp. 1041-1056. https://doi.org/10.1080/0020739X.2012.678896
Estimating winter crop area across seasons and regions using time-sequential MODIS imagery
Potgieter, Andries, Apan, Armando, Hammer, Graeme and Dunn, Peter. 2011. "Estimating winter crop area across seasons and regions using time-sequential MODIS imagery." International Journal of Remote Sensing. 32 (15), pp. 4281-4310. https://doi.org/10.1080/01431161.2010.486415
Expectations of Ability and Disability at University: The Fine Art of Managing Lives, Perceptions, and Curricula
Hammer, Sara, Werth, Shalene, Dunn, Peter, Lawson, Kym and d'Abadie, Danielle. 2011. "Expectations of Ability and Disability at University: The Fine Art of Managing Lives, Perceptions, and Curricula." Midgley, Warren, Tyler, Mark A., Danaher, Patrick Alan and Mander, Alison (ed.) Beyond Binaries in Education Research. New York, NY. United States. Routledge. pp. 211-220
Interspecific competition and small bird diversity in an urbanizing landscape
Kath, Jarrod, Maron, Martine and Dunn, Peter K.. 2009. "Interspecific competition and small bird diversity in an urbanizing landscape." Landscape and Urban Planning. 92 (2), pp. 72-79. https://doi.org/10.1016/j.landurbplan.2009.02.007
A statistical distribution for modelling rainfall with promising application in crop science
Lennox, Sarah, Dunn, Peter K., Power, Brendan and De Voil, Peter. 2004. "A statistical distribution for modelling rainfall with promising application in crop science." Fischer, Tony, Turner, Neil, Angus, John, McIntyre, Lynne, Robertson, Michael, Borrell, Andrew and Lloyd, David (ed.) 4th International Crop Science Congress (ICSC 2004): New Directions for a Diverse Planet. Brisbane, Australia 26 Sep - 01 Oct 2004 Gosford, Australia.
What Happens When a 1 × 1 × r Die is Rolled?
Dunn, Peter K.. 2003. "What Happens When a 1 × 1 × r Die is Rolled? " The American Statistician. 57 (4), pp. 258-264. https://doi.org/10.1198/0003130032332
Log-linear models
Dunn, Peter K.. 2004. "Log-linear models." Kempf-Leonard, Kimberley (ed.) Encyclopedia of social measurement. Dallas, TX. USA. Elsevier. pp. 585-589
Can offsets really compensate for habitat removal? The case of the endangered red-tailed black-cockatoo
Maron, Martine, Dunn, Peter K., McAlpine, Clive A. and Apan, Armando. 2010. "Can offsets really compensate for habitat removal? The case of the endangered red-tailed black-cockatoo." Journal of Applied Ecology. 47 (2), pp. 348-355. https://doi.org/10.1111/j.1365-2664.2010.01787.x
Early-season crop area estimates for winter crops in NE Australia using MODIS satellite imagery
Potgieter, A. B., Apan, A., Hammer, G. and Dunn, P.. 2010. "Early-season crop area estimates for winter crops in NE Australia using MODIS satellite imagery." ISPRS Journal of Photogrammetry and Remote Sensing. 65 (4), pp. 380-387. https://doi.org/10.1016/j.isprsjprs.2010.04.004
Commonality of rainfall variables influencing suspended solids concentrations in storm runoff from three different urban impervious surfaces
Brodie, Ian M. and Dunn, Peter K.. 2010. "Commonality of rainfall variables influencing suspended solids concentrations in storm runoff from three different urban impervious surfaces." Journal of Hydrology. 387 (3-4), pp. 202-211. https://doi.org/10.1016/j.jhydrol.2010.04.008
Tertiary students with a disability or chronic illness: stigma and study
Hammer, Sara, Werth, Shalene and Dunn, Peter. 2009. "Tertiary students with a disability or chronic illness: stigma and study." Bedford, Tas, Huijser, Henk and Muller, Sarah (ed.) Enabling Pathways: 3rd National Conference of Enabling Educators. Toowoomba, Australia 25 - 27 Nov 2009 Toowoomba, Australia.
Suspended particle characteristics in storm runoff from urban impervious surfaces in Toowoomba, Australia
Brodie, Ian M. and Dunn, Peter K.. 2009. "Suspended particle characteristics in storm runoff from urban impervious surfaces in Toowoomba, Australia." Urban Water Journal. 6 (2), pp. 137-146. https://doi.org/10.1080/15730620802541607
The impact of disabilities and long-term medical conditions on the student learning experience at USQ
Lawson, Kym, Werth, Shalene, Dunn, Peter and d'Abadie, Danielle. 2008. "The impact of disabilities and long-term medical conditions on the student learning experience at USQ." Pathways 9. Melbourne, Australia 02 - 05 Dec 2008 Melbourne, Australia.
Building-in quality rather than assessing quality afterwards: a technological solution to ensuring computational accuracy in learning materials
Dunn, Peter K.. 2008. "Building-in quality rather than assessing quality afterwards: a technological solution to ensuring computational accuracy in learning materials." Journal of Computers in Mathematics and Science Teaching. 27 (1), pp. 47-63.
Future scenarios for endangered species habitat in an intensifying agricultural landscape
Apan, Armando, Maron, Martine and Dunn, Peter. 2007. "Future scenarios for endangered species habitat in an intensifying agricultural landscape." ESA 2007: Adapting to Change. Perth, Australia 25 - 30 Nov 2007 Perth, Australia. Ecological Society of Australia.
Analysis of the rainfall data in Queensland using the Tweedie GLM
Ohnishi, Toshio and Dunn, Peter K.. 2007. "Analysis of the rainfall data in Queensland using the Tweedie GLM ." 2007 Japanese Joint Statistical Meeting. Kobe, Japan 06 - 09 Sep 2007 Japan.
Cloud observations for the statistical evaluation of the UV index at Toowoomba, Australia
Parisi, A. V., Sabburg, J., Turner, J. and Dunn, P. K.. 2008. "Cloud observations for the statistical evaluation of the UV index at Toowoomba, Australia." International Journal of Biometeorology: the description, causes, and implications of climatic change. 52 (3), pp. 159-166. https://doi.org/10.1007/s00484-007-0106-7
What happens with all that maths? (Part 2)
Dunn, Peter K.. 2004. "What happens with all that maths? (Part 2)." Teaching Mathematics. 29 (1), pp. 18-24.
What happens with all that maths?
Dunn, Peter K.. 2003. "What happens with all that maths?" Teaching Mathematics. 28 (4), pp. 29-34.
Continent-scale pattern in temporal dynamics of avian assemblages
Apan, Armando, Maron, Martine and Dunn, Peter K.. 2007. "Continent-scale pattern in temporal dynamics of avian assemblages." Bunce, R., Jongman, Rob, Hojas, L. and Weel, S. (ed.) IALE 2007: 25 Years Landscape Ecology: Scientific Principles in Practice. Wageningen, Netherlands 08 - 12 Jul 2007 Wageningen, Netherlands.
Estimating crop area using seasonal time series of Enhanced Vegetation Index from MODIS satellite imagery
Potgieter, Andries B., Apan, Armando, Dunn, Peter K. and Hammer, Graeme L.. 2007. "Estimating crop area using seasonal time series of Enhanced Vegetation Index from MODIS satellite imagery." Crop and Pasture Science. 58 (4), pp. 316-325. https://doi.org/10.1071/AR06279
Bootstrap confidence intervals for predicted rainfall quantiles
Dunn, Peter K.. 2001. "Bootstrap confidence intervals for predicted rainfall quantiles." International Journal of Climatology. 21 (1), pp. 89-94. https://doi.org/10.1002/joc.596
Calculus demonstrations using Matlab
Dunn, Peter K. and Harman, Chris. 2002. "Calculus demonstrations using Matlab." International Journal of Mathematical Education in Science and Technology. 33 (4), pp. 584-596. https://doi.org/10.1080/002073902320300856
Understanding statistics using computer demonstrations
Dunn, Peter K.. 2003. "Understanding statistics using computer demonstrations." Journal of Computers in Mathematics and Science Teaching. 22 (3), pp. 261-281.
Occurrence and quantity of precipitation can be modelled simultaneously
Dunn, Peter K.. 2004. "Occurrence and quantity of precipitation can be modelled simultaneously ." International Journal of Climatology. 24 (10), pp. 1231-1239. https://doi.org/10.1002/joc.1063
Statistical evaluation of data from tractor guidance systems
Dunn, Peter K., Powierski, Andrew P. and Hill, Rodger. 2006. "Statistical evaluation of data from tractor guidance systems." Precision Agriculture. 7 (3), pp. 179-192. https://doi.org/10.1007/s11119-006-9007-8
Series evaluation of Tweedie exponential dispersion model densities
Dunn, Peter K. and Smyth, Gordon K.. 2005. "Series evaluation of Tweedie exponential dispersion model densities." Statistics and Computing. 15 (4), pp. 267-280. https://doi.org/10.1007/s11222-005-4070-y
Identifying at-risk students: is it possible in a tertiary preparation course for adults?
Carmichael, Colin S., Dunn, Peter K. and Taylor, Janet A.. 2006. "Identifying at-risk students: is it possible in a tertiary preparation course for adults?" Grootenboer, Peter, Zevenbergen, Robyn and Chinnappan, Mohan (ed.) 29th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA29). Canberra, Australia 01 - 05 Jul 2006 Wahroonga, Sydney, Australia.
Power-variance models for modelling rainfall
Dunn, Peter K. and White, Neil. 2005. "Power-variance models for modelling rainfall." Francis, A. R., Matawie, K. M., Oshlack, A. and Smyth, Gordon K. (ed.) 20th International Workshop on Statistical Modelling. Sydney, Australia 10 - 15 Jul 2005
Spying on the winter wheat crop - generating objective planted area and crop production estimates using MODIS imagery
Potgieter, Andries B., Apan, Armando, Hammer, Graeme L. and Dunn, Peter K.. 2005. "Spying on the winter wheat crop - generating objective planted area and crop production estimates using MODIS imagery." Bellman, Chris, Cartwright, William and Shortis, Mark (ed.) 2005 Spatial Sciences Institute Biennial Conference: Spatial Intelligence, Innovation and Praxis (SSC2005). Melbourne, Australia 12 - 16 Sep 2005
We can still learn about probability by rolling dice and tossing coins
Dunn, Peter K.. 2005. "We can still learn about probability by rolling dice and tossing coins." Teaching Statistics. 27 (2), pp. 37-41. https://doi.org/10.1111/j.1467-9639.2005.00205.x