Related papers: Fat Tailed Distributions in Catastrophe Prediction
Catalytic prior distributions provide general, easy-to-use, and interpretable specifications of prior distributions for Bayesian analysis. They are particularly beneficial when the observed data are inadequate to stably estimate a complex…
We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…
In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
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…
Predicting the states of dynamic traffic actors into the future is important for autonomous systems to operate safelyand efficiently. Remarkably, the most critical scenarios aremuch less frequent and more complex than the uncriticalones.…
This paper explores the implications of producing forecast distributions that are optimized according to scoring rules that are relevant to financial risk management. We assess the predictive performance of optimal forecasts from…
Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular…
In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…
To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…
The noncentral $t$-distribution is a generalization of the Student's $t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral $t$-distribution which is…
An important question in health services research is the estimation of the proportion of medical expenditures that exceed a given threshold. Typically, medical expenditures present highly skewed, heavy tailed distributions, for which (a)…
We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…