Related papers: The distribution of aggregate storm risk in a chan…
Extratropical storms shape midlatitude weather and vary due to the slowly evolving climate and the rapid changes in synoptic conditions. While the influence of each factor has been studied extensively, their relative importance remains…
We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. The general solution of this equation for q=1 is a product of an…
This paper estimates local tornado risk from records of past events using statistical models. First, a spatial model is fit to the tornado counts aggregated in counties with terms that control for changes in observational practices over…
Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
We analyze the occurrence and the values of record-breaking temperatures in daily and monthly temperature observations. Our aim is to better understand and quantify the statistics of temperature records in the context of global warming.…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
The increasing occurrence of extreme weather events since the beginning of the 21st century has led to the development of new methods to attribute extreme events to anthropogenic climate change. The way in which the extreme event is defined…
Joint modelling of longitudinal observations and event times continues to remain a topic of considerable interest in biomedical research. For example, in HIV studies, the longitudinal bio-marker such as CD4 cell count in a patient's blood…
Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over…
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for…
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in $(0,1)$. All the sites are updated simultaneously at every discrete time. At any given time the environment may…
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with the…