In this paper we present a new type of multivariate distributions for asset returns which we call the multi-tail elliptical distributions. Multi-tail elliptical distribution can be thought to be an extension of the elliptical distributions that allow for varying tail parameters. We present a two-step random mechanism leading to this new type of distributions. In particular, this mechanism is de...

We propose a new family of distributions referred to as Weibull taildistributions. This family is designed to model left tails with exponential behavior. The exponent can be estimated using inference procedures adapted from the Weibull tail-distributions literature. Let us define a negative Weibull tail-distribution through its distribution function by: F (x) = exp {

To understand the interactions between the microtubule-based motor protein kinesin and intracellular components, we have expressed the kinesin heavy chain and its different domains in CV-1 monkey kidney epithelial cells and examined their distributions by immunofluorescence microscopy. For this study, we cloned and sequenced cDNAs encoding a kinesin heavy chain from a human placental library. T...

We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index α < 2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape of optimal paths; these are expressed in terms of a family (indexed by α) of “continuous last-passage percolation” models in the unit square. In the extreme cas...

The heavy tailed distributions have mostly been used for modeling the financial data. The kappa distribution has higher peak and heavier tail than the normal distribution. In this paper, we consider the estimation of the three unknown parameters of a Kappa distribution for evaluating the value at risk measure. The value at risk (VaR) as a quantile of a distribution is one of the import...

Let (Xn :n≥ 0) be a sequence of i.i.d. r.v.’s with negative mean. Set S0 = 0 and define Sn =X1 + · · ·+Xn. We propose an importance sampling algorithm to estimate the tail of M =max{Sn :n≥ 0} that is strongly efficient for both light and heavy-tailed increment distributions. Moreover, in the case of heavy-tailed increments and under additional technical assumptions, our estimator can be shown t...

We consider a (social) network whose structure can be represented by a simple random graph having a pre-specified degree distribution. A Markovian susceptible-infectious-removed (SIR) epidemic model is defined on such a social graph. We then consider two real-time vaccination models for contact tracing during the early stages of an epidemic outbreak. The first model considers vaccination of eac...

This paper derives a Cobb-Douglas matching function as the aggregate of the number of matches made by each firm in a large economy using results from the theory of heavy tail distributions. The model is then calibrated using the empirical distribution of firm sizes and stylized facts about social networks.The implied elasticity of the matching function is found to be close to those reported by ...

We consider a multi-station fluid model with arrivals generated by a big number of non-homogeneous heavy-tailed On/Off sources. If the model is feedforward in the sense that fluid cannot flow from one station to other with lighter tail distributions, we prove that under heavy-traffic, the scaled workload converges in distribution to a reflected fractional Brownian motion process with multidimen...

We provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices. Our estimates are based on in-fill asymptotics for directly identifying the jumps, together with Extreme Value Theory (EVT) approximations and methods-of-moments for assessing the tail decay parameters and tail dependencies. On implementing the procedures with a panel of intrada...