Especially for the 3-parameter Fréchet, the first quartile is and the third quartile
Also the quantiles for the mean and mode are:
Applications
Fitted cumulative Fréchet distribution to extreme one-day rainfalls
In
hydrology, the Fréchet distribution is applied to extreme events such as annually maximum one-day rainfalls and river discharges.[7] The blue picture, made with
CumFreq, illustrates an example of fitting the Fréchet distribution to ranked annually maximum one-day rainfalls in
Oman showing also the 90%
confidence belt based on the
binomial distribution. The cumulative frequencies of the rainfall data are represented by
plotting positions as part of the
cumulative frequency analysis.
However, in most hydrological applications, the distribution fitting is via the
generalized extreme value distribution as this avoids imposing the assumption that the distribution does not have a lower bound (as required by the Frechet distribution). [citation needed]
Fitted decline curve analysis. Duong model can be thought of as a generalization of the Frechet distribution.
In
decline curve analysis, a declining pattern the time series data of oil or gas production rate over time for a well can be described by the Fréchet distribution.[8]
One test to assess whether a multivariate distribution is asymptotically dependent or independent consists of transforming the data into standard Fréchet margins using the transformation and then mapping from Cartesian to pseudo-polar coordinates . Values of correspond to the extreme data for which at least one component is large while approximately 1 or 0 corresponds to only one component being extreme.
^
abMuraleedharan, G.; Guedes Soares, C.; Lucas, Cláudia (2011). "Characteristic and moment generating functions of generalised extreme value distribution (GEV)". In Wright, Linda L. (ed.). Sea Level Rise, Coastal Engineering, Shorelines, and Tides. Nova Science Publishers. Chapter 14, pp. 269–276.
ISBN978-1-61728-655-1.
^de Gusmão, Felipe R.S.; Ortega, Edwin M.M.; Cordeiro, Gauss M. (2011). "The generalized inverse Weibull distribution". Statistical Papers. 52 (3). Springer-Verlag: 591–619.
doi:
10.1007/s00362-009-0271-3.
ISSN0932-5026.
^Fréchet, M. (1927). "Sur la loi de probabilité de l'écart maximum". Ann. Soc. Polon. Math.6: 93.
^Fisher, R. A.; Tippett, L. H. C. (1928). "Limiting forms of the frequency distribution of the largest and smallest member of a sample". Proceedings of the Cambridge Philosophical Society. 24 (2): 180–190.
Bibcode:
1928PCPS...24..180F.
doi:
10.1017/S0305004100015681.
S2CID123125823.
^Gumbel, E. J. (1958). Statistics of Extremes. New York: Columbia University Press.
OCLC180577.
^Lee, Se Yoon; Mallick, Bani (2021). "Bayesian Hierarchical Modeling: Application Towards Production Results in the Eagle Ford Shale of South Texas". Sankhya B. 84: 1–43.
doi:
10.1007/s13571-020-00245-8.
Further reading
Kotz, S.; Nadarajah, S. (2000). Extreme Value Distributions: Theory and applications. World Scientific.
ISBN1-86094-224-5.
External links
Hurairah, Ahmed; Ibrahim, Noor Akma; bin Daud, Isa; Haron, Kassim (February 2005). "An application of a new extreme value distribution to air pollution data". Management of Environmental Quality. 16 (1): 17–25.
doi:
10.1108/14777830510574317.
ISSN1477-7835.
"wfrechstat: Mean and variance for the Frechet distribution". Wave Analysis for Fatigue and Oceanography (WAFO) (
Matlab software & docs). Centre for Mathematical Science. Lund University / Lund Institute of Technology. Retrieved 11 November 2023 – via www.maths.lth.se.
Especially for the 3-parameter Fréchet, the first quartile is and the third quartile
Also the quantiles for the mean and mode are:
Applications
Fitted cumulative Fréchet distribution to extreme one-day rainfalls
In
hydrology, the Fréchet distribution is applied to extreme events such as annually maximum one-day rainfalls and river discharges.[7] The blue picture, made with
CumFreq, illustrates an example of fitting the Fréchet distribution to ranked annually maximum one-day rainfalls in
Oman showing also the 90%
confidence belt based on the
binomial distribution. The cumulative frequencies of the rainfall data are represented by
plotting positions as part of the
cumulative frequency analysis.
However, in most hydrological applications, the distribution fitting is via the
generalized extreme value distribution as this avoids imposing the assumption that the distribution does not have a lower bound (as required by the Frechet distribution). [citation needed]
Fitted decline curve analysis. Duong model can be thought of as a generalization of the Frechet distribution.
In
decline curve analysis, a declining pattern the time series data of oil or gas production rate over time for a well can be described by the Fréchet distribution.[8]
One test to assess whether a multivariate distribution is asymptotically dependent or independent consists of transforming the data into standard Fréchet margins using the transformation and then mapping from Cartesian to pseudo-polar coordinates . Values of correspond to the extreme data for which at least one component is large while approximately 1 or 0 corresponds to only one component being extreme.
^
abMuraleedharan, G.; Guedes Soares, C.; Lucas, Cláudia (2011). "Characteristic and moment generating functions of generalised extreme value distribution (GEV)". In Wright, Linda L. (ed.). Sea Level Rise, Coastal Engineering, Shorelines, and Tides. Nova Science Publishers. Chapter 14, pp. 269–276.
ISBN978-1-61728-655-1.
^de Gusmão, Felipe R.S.; Ortega, Edwin M.M.; Cordeiro, Gauss M. (2011). "The generalized inverse Weibull distribution". Statistical Papers. 52 (3). Springer-Verlag: 591–619.
doi:
10.1007/s00362-009-0271-3.
ISSN0932-5026.
^Fréchet, M. (1927). "Sur la loi de probabilité de l'écart maximum". Ann. Soc. Polon. Math.6: 93.
^Fisher, R. A.; Tippett, L. H. C. (1928). "Limiting forms of the frequency distribution of the largest and smallest member of a sample". Proceedings of the Cambridge Philosophical Society. 24 (2): 180–190.
Bibcode:
1928PCPS...24..180F.
doi:
10.1017/S0305004100015681.
S2CID123125823.
^Gumbel, E. J. (1958). Statistics of Extremes. New York: Columbia University Press.
OCLC180577.
^Lee, Se Yoon; Mallick, Bani (2021). "Bayesian Hierarchical Modeling: Application Towards Production Results in the Eagle Ford Shale of South Texas". Sankhya B. 84: 1–43.
doi:
10.1007/s13571-020-00245-8.
Further reading
Kotz, S.; Nadarajah, S. (2000). Extreme Value Distributions: Theory and applications. World Scientific.
ISBN1-86094-224-5.
External links
Hurairah, Ahmed; Ibrahim, Noor Akma; bin Daud, Isa; Haron, Kassim (February 2005). "An application of a new extreme value distribution to air pollution data". Management of Environmental Quality. 16 (1): 17–25.
doi:
10.1108/14777830510574317.
ISSN1477-7835.
"wfrechstat: Mean and variance for the Frechet distribution". Wave Analysis for Fatigue and Oceanography (WAFO) (
Matlab software & docs). Centre for Mathematical Science. Lund University / Lund Institute of Technology. Retrieved 11 November 2023 – via www.maths.lth.se.