Robust stochastic modeling of speech is an important issue for the performance of practical applications. The Gaussian mixture model, GMM, is widely used in speaker ID, but its performance would get limited in the presence of unseen noise and distortions. Such noisy data, referred to as ”outliers” for the original distribution, can be better represented by the use of heavy-tail distributions, s...

The objective of this paper is to compare estimators which are a function of sample averages (a modification of Fan's estimators) based on different sample sizes for all symmetric stable distributions with exponent α (0 < α ≤ 2), according to the Pitman's measure of closeness criterion.

In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence that the probability distributions of the execution time of that algorithm exhibits a heavy tail with an hyperbolic probability decay for long executions, whic...

As well known, for a supercritical Galton–Watson process Zn whose offspring distribution has mean m > 1, the ratio Wn := Zn/m n has a.s. limit, say W . We study tail behaviour of the distributions of Wn and W in the case where Z1 has heavy-tailed distribution, that is, EeλZ1 = ∞ for every λ > 0. We show how different types of distributions of Z1 lead to different asymptotic behaviour of the tai...

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079–1084) states that if α̂n is an estimator of the tail index αP and {zn} is a sequence of positive numbers such that sup P∈Dr P(|α̂n − αP | ≥ zn) → 0, where Dr is a certain class of heavy-tailed distributions...

This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Though there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g. Processor Sharing and Shortest Remaining Processing Time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g. F...

We propose a class of alternative stochastic volatility models for electricity prices using the quantile function modeling approach. Specifically, we fit marginal distributions of power prices to two special classes of distributions by matching the quantile of an empirical distribution to that of a theoretical distribution. The distributions from the first class have closed-form formulas for pr...

Let Y be an Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dYt = a(Xt)Yt dt + σ(Xt)dWt, Y0 = y0. Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the stationary distribution of this model. A characterization of either heavy or light tail case is established. The method is based on a renewal theorem for systems of...

The empirical distribution of daily returns from financial market variables such as exchange rates, equity prices, and interest rates, is often skewed, having one heavy, and one semiheavy, or more Gaussian-like tail. The NIG distribution, that has two semi-heavy tails, models skewness rather well, but only in cases where the tails are not too heavy. On the other hand, the skew Student’s t-distr...

We establish a heavy-traffic asymptotic expansion (in powers of one minus the traffic intensity) for the asymptotic decay rates of queue-length and workload tail probabilities in stable infinite-capacity multi-channel queues. The specific model has multiple independent heterogeneous servers, each with i.i.d. service times, that are independent of the arrival process, which is the superposition ...