Alex J. Koning

Are Precipitation Levels Getting Higher? Statistical Evidence for the Netherlands

One of the possible consequences of global warming is that there will be more days with precipitation throughout the year, and also that the level of precipitation will be higher. In this paper a detailed statistical analysis of a century of daily precipitation levels is provided for the central meteorological station in the Netherlands. This paper shows that the often-considered gamma distribution does not fit well to samples of yearly data. It is argued that its incorrect use can lead to spuriously high probabilities of extreme precipitation levels. Relying on advanced nonparametric techniques, it is first found that there are fewer rainy days in the central part of the Netherlands. Next, more rainy days involve higher precipitation levels. Most importantly, no statistically significant shift is found in the annual largest values of daily rainfall over the course of the century, which suggest that the probability of extremely high levels has not changed over time.

Tail behaviour of Gaussian processes with applications to the Brownian pillow

In this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes ocurring in nonparametric testing of [multivariate] indepencency and [multivariate] constancy over time. The tail behaviour of S is described by means of a constant a and a random variable R which is defined on the same probability space as S. The constant a acts as an upper bound, and is relevant for the computation of the efficiency of test statistics converging in distribution to S. The random variable R acts as a lower bound, and is instrumental in deriving approximations for the upper percentage points of S by simulation.

An improved method for forecasting spare parts demand using extreme value theory

Inventory control for spare parts is essential for many organizations due to the trade-off between preventing high holding cost and stockouts. The lead time demand distribution plays a central role in inventory control. The estimation of this distribution is problematic as the spare part demand is often intermittent, and as a consequence often only a limited number of non-zero data points are available in practice. The well-known empirical method uses historical demand data to construct the lead time demand distribution. Although it performs reasonably well when service requirements are relatively low, it has difficulties in achieving high target service levels. In this paper, we improve the empirical method by applying extreme value theory to model the tail of the lead time demand distribution. To make the most out of a limited number of demand observations, we establish that extreme value theory can be applied to lead time demand periods computed over overlapping intervals. We consider two service levels: the expected waiting time and cycle service level. Our experiments show that our method improves the inventory performance compared to the empirical method and is competitive with the WSS method, Croston’s method and SBA for a range of demand distributions.

Generalized Bi-Additive Modelling for Categorical Data

Generalized linear modelling (GLM) is a versatile technique, which may be viewed as a generalization of well-known techniques such as least squares regression, analysis of variance, loglinear modelling, and logistic regression. In may applications, low-order interaction (such as bivariate interaction) terms are included in the model. However, as the number of categorical variables increases, the total number of low-order interactions also increases dramatically. In this papaer, we propose to constrain bivariate interactions by a bi-additive model which allows a simple graphical representation in which each category of every variable is represented by a vector.

Analyzing preferences ranking when there are too many alternatives.

Consumer preferences can be measured by rankings of alternatives. When there are too many alternatives, this consumer task becomes complex. One option is to have consumers rank only a subset of the available alternatives. This has an impact on subsequent statistical analysis, as now a large amount of ties is observed. We propose a simple methodology to perform proper statistical analysis in this case. It also allows to test whether (parts of the) rankings are random or not. An illustration shows its ease of application.