In the presence of a heavy-tail noise distribution, regression becomes much more difficult. Traditional robust regression methods assume that the noise distribution is symmetric, and they downweight the influence of so-called outliers. When the noise distribution is asymmetric, these methods yield biased regression estimators. Motivated by data-mining problems for the insurance industry, we pro...

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that heavy tail distribution produces an extremely slow dynamics, resulting in singular large deviation function. When singularity takes place, bottom function flattened, manifesting anomalous fluctuations processes. In this article, we aim to how these singularities emerge ...

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have unproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or...

Removing noise from images is a challenging problem in digital image processing. This paper presents an image denoising method based on a maximum a posteriori (MAP) density function estimator, which is implemented in the wavelet domain because of its energy compaction property. The performance of the MAP estimator depends on the proposed model for noise-free wavelet coefficients. Thus in the wa...

PhFit, a new Phase-type fitting tool is presented in this paper. PhFit allows for approximating distributions or set of samples not only by continuous but by discrete Phasetype distributions as well. The implemented algorithms separate the fitting of the body and the tail part of the distribution which results in satisfactory fitting also for heavy-tail distributions. Moreover, PhFit allows the...

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails ...

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are projected onto Gaussian distributions. Here, we offer an important generalization to the case where er...

Heavy tails in work loads (file sizes, flow lengths, service times, etc.) have significant negative impact on the performance of queues and networks. In the context of the famous Internet file size data of Crovella and some very recent data sets from a wireless mobility network, we examine the new class of LogPH distributions introduced by Ramaswami for modeling heavy tailed random variables. T...

For heavy-tailed econometric data it is of interest to estimate the tail index, a parameter that measures the thickness of the tails of the marginal distribution. Common models for such distributions include Pareto and t distributions, and in other applications (such as hydrology) stable distributions are popular as well. This paper constructs square root n consistent estimators of the tail ind...