The use of GEV and GPD has received much attention in hydrology for use in extreme precipitation and flood analysis. Methods of parameter estimates such as Maximum Likelihood Estimates and Linear Moments have been used and even metastatistics has also come up. My problem is that, these methods haven't been used in the analysis of water quality extremes. It is my hope to get an appropriate method which can be replicated to use. Please help!
Hi Nsiah,
Firstly you would need to define the problem you want to model then you would need to find an appropriate model for the system. Statistics of extremes have been applied to a large type of problems in all kind of physical systems, have a look at a similar question published in RG about a month ago:
https://www.researchgate.net/post/How_do_you_think_about_the_applicability_of_Extreme_Value_theory_on_water_quality_management
Hope it helps,
Augusto
Hi Nsiah,
Firstly you would need to define the problem you want to model then you would need to find an appropriate model for the system. Statistics of extremes have been applied to a large type of problems in all kind of physical systems, have a look at a similar question published in RG about a month ago:
https://www.researchgate.net/post/How_do_you_think_about_the_applicability_of_Extreme_Value_theory_on_water_quality_management
Hope it helps,
Augusto
I think this might be a good starting point:
D.R. Helsel and R.M. Hirsch. 2002. Statistical Methods in Water Resources. U.S. Geological Survey, Techniques of Water-Resources Investigations Book 4, Chapter A3.
pdf download available at https://pubs.usgs.gov/twri/twri4a3/
ITRC also has some good documents and internet training (I think most of it is free but not positive. Go to:
https://www.itrcweb.org/Team/Public?teamID=10
Scroll down to middle of page and click on the 2 hyperlinks:
'Groundwater Statistics and Monitoring Compliance (GSMC-1)' and 'Internet-based training course'
After this, probably best to get advice from the statistical experts.
Hope this helps.
Thanks to all (Dr, Sanabria, Mohammed Zakwan & Jiheon) for the remarkable responses you are contributing. Infact i am excited and believe my research problem will come out more clearer with the help of YOUR wonderful reponses.
My concern now is with the "Time Step" of the data and the most "Preferred Method" for the parameter estimates. Can YOU suggest appropriate research papers?
I think an appropriate first step is to determine if your data require and extreme value distribution. E.g. are your data well fit by a log normal distribution. L-moments are useful tools for screening candidate distributions (see, e.g. Handbook of Hydrology). Use & estimation of Extreme value distributions is well chronicled in work of Katz. See, e.g. Climatic Change 100:71-76 / DOI 10.1007/s10584-010-9834-5 , and the NCAR R software package extRemes: http://www.ral.ucar.edu/~ericg/extRemes/
Hi Nsiah,
The literature on the statistics of extremes is rather large. The R system has a lot of packages to apply the statistics of extremes to practical problems. Go to "CRAN", then "search" and enter "extremes". An R package I highly recommend is "extRemes" which is described in: 1) https://www.jstatsoft.org/article/view/v072i08.
2) You can also look at the classic: Coles S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.
3) A comprehensive review of techniques to apply the statistics of extremes (in wind engineering) is in: Palutikof (1999)Article A review of methods to calculate extreme wind speeds
Hope it helps,
Augusto
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