Related papers: Alternative modelling and inference methods for cl…
We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account…
In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly…
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally…
The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
The Zipf distribution also known as scale-free distribution or discrete Pareto distribution, is the particular case of Power Law distribution with support the strictly positive integers. It is a one-parameter distribution with a linear…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic…
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…
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…
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely…
The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
Continuous mixtures of distributions are widely employed in the statistical literature as models for phenomena with highly divergent outcomes; in particular, many familiar heavy-tailed distributions arise naturally as mixtures of…
In the present paper, we discuss contra-arguments concerning the use of Pareto-Lev\'y distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data.…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we…