Heavy-tailed distributions have been used tomodel phenomena in which extreme events occur with high probability. In these type of occurrences, it is likely that extreme events are not observable after a certain threshold. Appropriate estimators are needed to deal with this type of censored data. We show that the well-known Hill-Hall estimator is unable to deal with censored data and yields high...

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geome...

Abstract We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue a different way. Inter-event times all are Mittag-Leffler distributed, which is heavy tail distribution with no moments. For of we answer question being at zero infinitely often (the ‘recurrence’ regime) or not transient regime). Aside from this question, analytical propertie...

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness have received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of...

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account the heavy tail phenomenon of stock returns. Recently, robust estimator was handle heavy-tailed di...

We study Markov chain Monte Carlo (MCMC) algorithms for target distributions defined on matrix spaces. Such an important sampling problem has yet to be analytically explored. carry out a major step in covering this gap by developing the proper theoretical framework that allows identification of ergodicity properties typical MCMC algorithms, relevant such context. Beyond standard Random-Walk Met...

Combinatorial search methods often exhibit a large variability in performance. We study the cost prooles of combinatorial search procedures. Our study reveals some intriguing properties of such cost prooles. The distributions are often characterized by very long tails or \heavy tails". We will show that these distributions are best characterized by a general class of distributions that have no ...

Note that the function φ(γ) is monotone continuous in the interval (−∞, γ̂), and φ(γ̂) = limγ↑γ̂ φ(γ) ∈ [1,∞]. We distinguish all the distributions on [0,∞) according to the value of γ̂. If γ̂ = 0, then we say that the distribution F is heavy-tailed ; in that case φ(γ) =∞ for any γ > 0. If γ̂ > 0, then we call the distribution F light-tailed ; this happens if and only if, for some γ > 0, F (x) = o(e−...

Let (Xn : n ≥ 0) be a sequence of iid rv’s with mean zero and finite variance. We present an efficient statedependent importance sampling algorithm for estimating the tail of Sn = X1 + ...+Xn in a large deviations framework as n ↗ ∞. Our algorithm can be shown to be strongly efficient basically throughout the whole large deviations region as n ↗ ∞ (in particular, for probabilities of the form P...

This paper presents a simple boundedly rational model of a firm and consumer behaviour. We formulate an entry game, where every firm decides on investing in R&D for inventing a new product that will appeal to certain group of consumers. The success depends on the amount of funds available for the project as well as firm’s familiarity with the relevant proportion of taste space. We identify the ...