Forecasting and Assessing Risk of Individual Electricity Peaks by Maria Jacob & Cláudia Neves & Danica Vukadinović Greetham

Author:Maria Jacob & Cláudia Neves & Danica Vukadinović Greetham
Language: eng
Format: epub
ISBN: 9783030286699
Publisher: Springer International Publishing

2.to find all the possible distributions that may occur in the limit and derive a generalised form for those distributions.

The first goal is known as the domains of attraction problem whereas the second is known as the limit problem. Before we take a look at the asymptotic theory, it is valuable to review some of the statistical background and terminology that will be prevalent throughout this report.

The rest of this chapter is dedicated to an in depth exploration of extreme value theory, particularly the probabilistic foundations for the methods of inference presented in Chap. 4 and ensuing application in Chap. 5. In the following section, we will introduce and clarify some of the central terminology and nomenclature. In Sect. 3.2, we will explore the fundamental extreme value theorem which gives rise to the generalised form to the limiting distribution of sample maxima and other relevant results. We will then consider results for the Peaks over threshold (POT) approach in Sect. 3.3. In Sect. 3.4, some theory on regularly varying functions is discussed. The theory of regular variation is quite central to EVT though often it operates from the background. Familiarity with regular variation is highly recommended for the readers interested in a mathematical and theoretical treatment of EVT. Finally, in Sect. 4.​4, we consider the case where condition of identically distributed rv’s can be relaxed. In Chaps. 3 and 4 as a whole, we aim to provide intuitive understanding of the theoretical results, to expound reasons for these being in great demand to many applications and to illustrate them with some examples of challenges arising in the energy sector.

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