Estimating the extreme value index for imprecise data

In extreme value theory the focus is on the tails of the distribution. The main focus is to estimate the tail distribution for a rounded data set. To estimate this tail distribution the extreme value index should be estimated, but due to the rounded data this extreme value index oscillates heavily. Therefore a correct estimate can not be...

Estimating the expected shortfall using extreme value theory

The behavior of the conditional expectation of X given that X exceeds the (1-p)'th quantile, where p descends to 0, has been analyzed. Some already know that this special conditional expectation has been given the name: Expected shortfall. Under certain assumptions, a limit is derived for the expected shortfall as p decreases to 0 and from this...

Non-parametric extreme quantile estimation for the common shaped tail model: Forecasting extreme precipitation by post-processing precipitation from a numerical weather prediction model

The estimation of extreme quantile curves of a family of conditional distributions is a non-trivial problem, due to the data-sparseness in the tail of the distribution. This thesis considers the problem of post-processing extreme precipitation forecasts in Friesland from the numerical weather prediction model HARMONIE. Assuming forecasts are...

Voorspellen van veel neerslag: gebruikmakend van regressieanalyse en de ECMWF-modeluitvoer

In deze scriptie is onderzocht of regressie, een postprocessing methode, een goede toevoeging is aan het model dat het Europees Centrum voor Weersverwachtingen op Middellange Termijn (ECMWF) ontwikkeld heeft en waarvan het KNMI de uitvoer gebruikt, specifiek om te bepalen of er minstens 5 mm neerslag op een dagdeel (00-12 UTC en 12-00 UTC) zal...

Ordering multivariate observations by data depth

In this thesis the theory of depth functions is researched. Depth functions are functions that measure data depth and order multivariate observations. Two depth functions are discussed: the halfspace and simplicial depth function. The halfspace depth of a point is defined as the smallest probability for which a closed halfspace contains that...

Comparison on estimations for the extremal index: Vergelijken van schatters van de extreme index

The clustering of events can have a large impact on society. The extremal index $\theta$ tells how much extreme events cluster. We will compare different types of estimators in this project. First, we review the extremes of different sequences which have different values of $\theta$. We have found significant differences between the extremes....

Customer segmentation using RFM analysis

This paper is a research on the segmentation of customers. The clustering of customers is done based on the variables recency, frequency and monetary value. Such a clustering is called an RFM-model. The clustering is done using the K-means clustering method. To find the optimal number of clusters the following performance metrics are used: Elbow...