Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.

On the Skew-Normal-Cauchy Distribution

In this article, we study further properties of a skew normal distribution, called the skew-normal-Cauchy (SNC) distribution by Nadarajah and Kotz (2003). A stochastic representation is obtained which allows alternative derivations for moments, moments generating function, and skewness and kurtosis coefficients. Issues related to singularity of the Fisher information matrix are investigated.

A New Class of Non Negative Distributions Generated by Symmetric Distributions

In this article, we study a new class of non negative distributions generated by the symmetric distributions around zero. For the special case of the distribution generated using the normal distribution, properties like moments generating function, stochastic representation, reliability connections, and inference aspects using methods of moments and maximum likelihood are studied. Moreover, a real data set is analyzed, illustrating the fact that good fits can result.

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

The beta-Birnbaum-Saunders distribution An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies For the first time based on this distribution the so-called beta-Birnbaum-Saunders distribution is proposed for fatigue life modeling Various properties of the new model including expansions for the moments moment generating function mean deviations density function of the order statistics and their moments are derived We discuss maximum likelihood estimation of the model s parameters The superiority of the new model is illustrated by means of three failure real data sets (C) 2010 Elsevier B V All rights reserved

The beta Laplace distribution

The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set. (C) 2011 Elsevier B.V. All rights reserved.

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Radii in weakly-bound light halo nuclei

A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of Li-11 and Be-14 nuclei. (C) 2004 Published by Elsevier B.V.

Scaling in few-body nuclear physics

The nuclear matter calculations with realistic nucleon-nucleon potentials present a general scaling between the nucleon-nucleus binding energy, the corresponding saturation density, and the triton binding energy. The Thomas-Efimov three-body effect implies in correlations among low-energy few-body and many-body observables. It is also well known that, by varying the short-range repulsion, keeping the two-nucleon information (deuteron and scattering) fixed, the four-nucleon and three-nucleon binding energies lie on a very narrow band known as a Tjon line. By looking for a universal scaling function connecting the proper scales of the few-body system with those of the many-body system, we suggest that the general nucleus-nucleon scaling mechanism is a manifestation of a universal few-body effect.

EXOTIC CARBON SYSTEMS IN TWO-NEUTRON HALO THREE-BODY MODELS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universality and Scaling Limit of Weakly-Bound Tetramers

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B-3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited N-th tetramer energy B-4((N)) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B-4((N))/B-3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

Binding and structure of tetramers in the scaling limit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Statistical properties of a dissipative kicked system: Critical exponents and scaling invariance

A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action. (C) 2012 Elsevier B.V. All rights reserved.

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the triatomic molecules 4He 3, 4He 2- 6Li, 4He 2- 7Li, and 4He 2- 23Na were calculated using a renormalized three-body model with a pairwise Dirac-δ interaction, having as physical inputs only the values of the binding energies of the diatomic and triatomic molecules. Molecular three-body systems with bound subsystems were considered. The resultant data were analyzed in detail.

Three-body recombination in ultracold systems: Prediction of weakly-bound atomic trimer energies

The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E 3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein condensates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation.