Abstract
Probability plots allow for a straightforward analysis of the data and interpretation of results also by non-statisticians and still play a central role in today’s software. In this chapter, probability plots for extreme value (EV) distributions are developed based on the generalized least-squares distribution fitting method and on convenient approximations of the first two moments of order statistics from the standard EV distributions. The proposed probability plots lead to graphical estimators of parameters that are shown to be nearly unbiased through the use of pivotal indices that avoid the massive numerical investigations usually presented for similar purposes in the recent literature. Although more efficient biased solutions can be theoretically found, the obtained parameter estimators achieve also adequate performances in terms of mean square deviation with respect to those derived through probability plots that have been presented separately in the literature as the most effective for EV distributions. Lastly, a real-case study is presented concerning wind speed data collected at a candidate wind farm site in Southern Italy. The results demonstrate how the proposed probability plot can effectively support EV analysis and assist practitioners in the selection of the turbine class to be installed.
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Acknowledgements
The author is extremely grateful to the Editor and the anonymous reviewers for their valuable suggestions as well as to Professor Pasquale Erto for his continuous criticism and insight that significantly contributed to improve the chapter. The author also deeply thanks Ten Project S.r.l. (www.tenproject.it) for providing with the anemometric data and the engineer Massimo Lepore (Renewable Energy Source Systems) for his experienced discussion useful in defining the case study.
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Lepore, A. (2019). Nearly Unbiased Probability Plots for Extreme Value Distributions. In: Petrucci, A., Racioppi, F., Verde, R. (eds) New Statistical Developments in Data Science. SIS 2017. Springer Proceedings in Mathematics & Statistics, vol 288. Springer, Cham. https://doi.org/10.1007/978-3-030-21158-5_34
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