Statistical estimations for probability distributions having tails of special shape, such as a double-mode distri-bution well the so-called heavy-tailed or fat-tailed distribution, are quantitatively discussed through virtual experiments using computer simulations. In this paper, distribution describing damage degree concrete liners tunnels in cold region is examined an example distribution. Fi...

A system with heavy tailed service requirements under heavy load having a single server, has an equilibrium waiting time distribution which is approximated by the Mittag{Leeer distribution. This fact is understood by a direct analysis of the weak convergence of a sequence of negative drift random walks with heavy right tail and the associated all time maxima of these random walks. This approach...

We present new excess risk bounds for randomized and deterministic estimators for general unbounded loss functions including log loss and squared loss. Our bounds are expressed in terms of the information complexity and hold under the recently introduced v-central condition, allowing for high-probability bounds, and its weakening, the v-pseudoprobability convexity condition, allowing for bounds...

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural MRI and functional fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and across spatial locations. An anatomic...

In modeling evolutionary genetics, it is often assumed that mutational effects are assigned according to a continuous probability distribution, and multiple distributions have been used with varying degrees of justification. For mutations with beneficial effects, the distribution currently favored is the exponential distribution, in part because it can be justified in terms of extreme value the...

In this paper we study the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, we obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, we...

Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total ris...

We study Random 2-SAT problem, in which 2-CNFs are sampled from a wide range of non-uniform distributions, including heavy-tailed using random model that is quite different the standard uniform 2-SAT. This SAT so-called configuration model, given by distribution ξ for degree (or number occurrences) each variable. To generate formula variable , generating several clones Then 2-clauses created ch...

In this paper, we consider some non-standard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim-size distribution belongs to some classes of heavy-tailed distributions and a constrai...

Extreme losses of portfolios with heavy-tailed components are studied in the framework of multivariate regular variation. Asymptotic distributions of extreme portfolio losses are characterized by a functional γξ = γξ(Ψ, α) of the tail index α, the spectral measure Ψ, and the vector ξ of portfolio weights. Existence, uniqueness, and location of the optimal portfolio are analysed and applied to t...