Income distributions are usually characterised by a heavy right-hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distribu...

different samples have been prepared from different products in chadormalu iron ore concentrator plant: low intensity magnetite separators concentrate (magnetite concentrate), reverse flotation tail (final hematite concentrate), flotation concentrate (apatite concentrate), final tail (l.i.m.s. tail + reverse flotation concentrate+ apatite flotation tail). the samples were used for rare earth el...

Since the work of Mandelbrot in the 1960’s there has accumulated a great deal of empirical evidence for heavy tailed models in finance. In these models, the probability of a large fluctuation falls off like a power law. The generalized central limit theorem shows that these heavy-tailed fluctuations accumulate to a stable probability distribution. If the tails are not too heavy then the varianc...

In this paper, we are analyzing the interactivity time, defined as the duration between two consecutive tasks such as sending emails, collecting friends and followers and writing comments in online social networks (OSNs). The distributions of these times are heavy tailed and often described by a power-law distribution. However, powerlaw distributions usually only fit the heavy tail of empirical...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of t...

Bayesian estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior distributions of the tail index and their consistency and asymptotic normality are established. Finitesample properties of the proposed estimators are investigated via simulations. Tail index...

We study the transport of collective excitations (Frenkel excitons) in systems with static disorder in the transition energies, not limiting ourselves to Gaussian transition energy distributions. Instead, we generalize this model to the wider class of Lévy stable distributions, characterized by heavy tails. Phonon-assisted scattering of excitons, localized by the disorder, leads to thermally ac...

In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of r...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and Value-at-Risk is derived for heavy tailed l...