相关论文: Indirect identification of damage functions from d…
We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…
We study the statistics of human deaths from wars, conflicts, similar man-made conflicts as well as natural disasters. The probability distribution of number of people killed in natural disasters as well as man made situations show power…
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 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…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
The distribution of the magnitudes of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded close to the point at which the system fails catastrophically, we find that the power law has…
Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events…
Reliable estimates of indirect economic losses arising from natural disasters are currently out of scientific reach. To address this problem, we propose a novel approach that combines a probabilistic physical damage catastrophe model with a…
Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function $f \ge 0$. From an application point of view, one is rather interested in extreme loss events that occur relative to…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
Several groups have recently investigated the flow of information in high-energy collisions, from the entanglement entropy of the proton yielding classical Shannon entropy of its parton distribution functions (pdfs), through jet splitting…
We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing…
We propose extreme value analogues of natural exponential families and exponential dispersion models, and introduce the slope function as an analogue of the variance function. The set of quadratic and power slope functions characterize…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…