TY - THES ID - 134550928 TI - Estimating the maximal earthquake magnitude using extreme value theory AU - Decuypere, Simon AU - Beirlant, Jan. AU - KU Leuven. Faculteit Wetenschappen. Opleiding Master in de wiskunde (Leuven) PY - 2016 PB - Leuven KU Leuven. Faculteit Wetenschappen DB - UniCat UR - https://www.unicat.be/uniCat?func=search&query=sysid:134550928 AB - In many distributions, natural upper bounds can appear that truncate the probability tail, and ultimately at the largest data, deviations from a Pareto tail behaviour can become apparent. We use the term truncation to indicate that it's only possible to observe outcomes above or below a certain truncation limit. Quite similarly, a truncated distribution is a conditional distribution, which results from restricting the domain of some other probability distribution. In this master's thesis, we're going to direct our attention to one field in particular: we're going to investigate and analyse several estimation techniques for -the existence of- the maximum possible earthquake magnitude in a certain area. We will discuss the Gutenberg-Richter distribution: a doubly truncated exponential distribution which is extremely important in the discussion of earthquake magnitudes. The Gutenberg-Richter model is widely used and has been shown to fit both worldwide and regional earthquake catalogues. Here, we will also discuss some already existing non-parametric estimators for estimating the maximum possible magnitude. The great attraction of these non-parametric estimators is that they do not require any specific functional form for the magnitude distribution. As such, these estimators are able to deal with distributions of any complexity. Next, we'll discuss estimators based on Extreme Value Theory (EVT), which is the branch of statistics that deals with extreme deviations from the median of probability tails. Its primary goal is to find the probability of events that are more extreme than any previously observed. We will present and discuss some famous results in EVT, as well as introduce some of the most commonly used distributions in the domain, like the Generalized Extreme Value (GEV) distribution and the Generalized Pareto Distribution (GPD). In that same context, we'll also discuss some classical empirical tools like the mean excess plot and the Pareto QQ-plot, together with some classical results concerning the estimation of the Extreme Value Index (EVI) such as Hill's estimator, as well as analyse some of the more recent work concerning the estimation of the truncation limit and the EVI. Based on results from EVT, we will discuss a first method which will require the use of a truncated Pareto distribution with a positive tail index and a second more general method, valid for any max-domain of attraction with an EVI >-1/2. For both methods, we'll discuss an estimator for the endpoint, for the EVI and for the quantiles as well. These two methods, as long as certain conditions are fulfilled, can be applied in any field for investigating truncation. In this master's thesis, we also make use of the Gutenberg-Richter law, which serves as a connection between the energy and the magnitudes of earthquakes. Based on several simulations, we concluded that EVT methods can in fact perform better for certain values of k than the non-parametric ones, with k being the amount of largest observations that one uses. We applied all our findings to magnitude data from Groningen, where earthquakes are happening more frequently due to human activity. ER -