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## A new family of generalized distributions

CORDEIRO, Gauss M.; CASTRO, Mario de
Fonte: TAYLOR & FRANCIS LTD Publicador: TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.24%
Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix Kw) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.; CNPq, Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

## Random number generators for the generalized Birnbaum-Saunders distribution

LEIVA, Victor; SANHUEZA, Antonio; SEN, Pranab K.; PAULA, Gilberto A.
Fonte: TAYLOR & FRANCIS LTD Publicador: TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.1%
The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.; FONDECYT[1050862]; FONDECYT; FANDES[C-13955(10)]; FANDES; DIPUV[42-2004]; DIPUV; DIUFRO[120321]; DIUFRO; CAPES; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Fapesp...

## An R implementation for generalized Birnbaum-Saunders distributions

BARROS, Michelli; PAULA, Gilberto A.; LEIVA, Victor
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.14%
The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. in this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed. (C) 2008 Elsevier B.V. All rights reserved.; FONDECYT; FONDECYT[1080326]; DIPUV, Chile[29-2006]; DIPUV, Chile; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); FAPESP grants, Brazil; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

## The new class of Kummer beta generalized distributions

Pescim, Rodrigo Rossetto; Cordeiro, Gauss Moutinho; Demetrio, Clarice Garcia Borges; Ortega, E. M. M.; Nadarajah, S.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.19%
Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.; CNPq (Brazil); CNPq (Brazil)

## Generalized beta-generated distributions

Alexander, Carol; Cordeiro, Gauss M.; Ortega, Edwin Moises Marcos; Maria Sarabia, Jose
Fonte: ELSEVIER SCIENCE BV; AMSTERDAM Publicador: ELSEVIER SCIENCE BV; AMSTERDAM
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.12%
This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.; Ministerio de Educacion of Spain [PR2009-0200, ECO2010-15455]; Ministerio de Educacion of Spain; CNPq-Brazil; CNPq (Brazil)

## Introdução às equações diferenciais ordinárias no contexto das funções generalizadas temperadas de Colombeau; Introduction to the ordinary differential equation in the framework of Colombeau's tempered generalized functions

França, Sávio Mendes
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
36.25%

## A distribuição beta generalizada semi-normal; The beta generalized half-normal distribution

Pescim, Rodrigo Rossetto
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
36.24%

## Distribuição exponencial generalizada: uma análise bayesiana aplicada a dados de câncer; Generalized exponential distribution: a Bayesian analysis applied to cancer data

Boleta, Juliana
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
36.1%

## Distribuições das classes Kumaraswamy generalizada e exponenciada: propriedades e aplicações; Distributions of the generalized Kumaraswamy and exponentiated classes: properties and applications

Braga Junior, Antonio Carlos Ricardo
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
36.1%

## The new class of Kummer beta generalized distributions: theory and applications; A nova classe de distribuições Kummer beta generalizada: teoria e aplicações

Pescim, Rodrigo Rossetto
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
46.22%
In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets.; Neste trabalho...

## Bayesian estimation of generalized exponential distribution under noninformative priors

Moala, Fernando Antonio; Achcar, Jorge Alberto; Damasceno Tomazella, Vera Lucia; Stern, JM; Lauretto, MD; Polpo, A; Diniz, MA
Fonte: Amer Inst Physics Publicador: Amer Inst Physics
Tipo: Conferência ou Objeto de Conferência Formato: 230-242
ENG
Relevância na Pesquisa
36.12%
The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

## Generalized-generalized entropies and limit distributions

Thurner,Stefan; Hanel,Rudolf
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
36.14%
Limit distributions are not limited to uncorrelated variables but can be constructively derived for a large class of correlated random variables, as was shown e.g. in the context of large deviation theory [1], and recently in a very general setting by Hilhorst and Schehr [2]. At the same time it has been conjectured, based on numerical evidence, that several limit distributions originating from specific correlated random processes follow q-Gaussians. It could be shown that this is not the case for some of these situations, and more complicated limit distributions are necessary. In this work we show the derivation of the analytical form of entropy which -under the maximum entropy principle, imposing ordinary constraints- provides exactly these limit distributions. This is a concrete example for the necessity of more general entropy functionals beyond q statistics.

## Generalized Parton Distributions and Hadronic Observables

Ahmad, S.; Honkanen, H.; Liuti, S.; Taneja, S. K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.19%
Following a previous detailed study of unpolarized generalized parton distribution functions in the non-singlet sector, and at zero values of the skewness variable, $\zeta$, we propose a physically motivated parametrization that is valid at $\zeta \neq 0$. Our method makes use of information from the nucleon form factor data, from deep inelastuc scattering parton distribution functions, and from lattice results on the Mellin moments of generalized parton distributions. It provides, therefore, a step towards a model independent extraction of generalized distributions from the data, alternative to the mathematical ansatz of double distributions. Comparisons with recent experimental data on the proton are shown.; Comment: Proceedings of Workshop on "Exclusive Reactions at High Momentum Transfer", May 21-24, 2007, Jefferson Lab, Newport News, VA USA

## Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.26%
We propose a physically motivated parametrization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, \zeta. Our approach follows a previous detailed study of the \zeta=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non singlet sector. Additional constraints at \zeta \neq 0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards a model independent extraction of generalized distributions from the data. It also provides an alternative to double distributions based phenomenological models in that we are able to satisfy the polynomiality condition by construction, using a combination of experimental data and lattice, without resorting to any specific mathematical construct.; Comment: 29 pages, 8 figures; added references...

## Energy of generalized distributions

González-Dávila, J. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.14%
We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint closed submanifolds. We derive a lower bound for the energy of all $q$-dimensional almost regular distributions, for each $q< \dim M,$ and find several examples of foliations which minimize the energy functional over certain sets of smooth generalized distributions.; Comment: 19 pages

## Bose-Einstein and Fermi-Dirac distributions in nonextensive quantum statistics: Exact and interpolation approaches

Hasegawa, Hideo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.19%
Generalized Bose-Einstein (BE) and Fermi-Dirac (FD) distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation [Rajagopal, Mendes, and Lenzi, Phys. Rev. Lett. {\bf 80}, 3907 (1998)]. It has been shown that the $(q-1)$ expansion in the exact approach agrees with the result obtained by the asymptotic approach valid for $O(q-1)$. Model calculations have been made with a uniform density of states for electrons and with the Debye model for phonons. Based on the result of the exact approach, we have proposed the {\it interpolation approximation} to the generalized distributions, which yields results in agreement with the exact approach within $O(q-1)$ and in high- and low-temperature limits. By using the four methods of the exact, interpolation, factorization and superstatistical approaches, we have calculated coefficients in the generalized Sommerfeld expansion, and electronic and phonon specific heats at low temperatures. A comparison among the four methods has shown that the interpolation approximation is potentially useful in the nonextensive quantum statistics. Supplementary discussions have been made on the $(q-1)$ expansion of the generalized distributions based on the exact approach with the use of the un-normalized MEM...

## Generalized Parton Distributions from Hadronic Observables

Ahmad, S.; Honkanen, H.; Liuti, S.; Taneja, S. K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.14%
We propose a physically motivated parametrization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, \zeta. At \zeta=0, H and E are determined using constraints from simultaneous fits of experimental data on both the nucleon elastic form factors and the deep inelastic structure functions. Lattice calculations of the higher moments constrain the parametrization at \zeta > 0. Our method provides a step towards a model independent extraction of generalized distributions from the data that is alternative to the mathematical ansatz of double distributions.; Comment: 4 pages, 2 figures, to appear in the proceedings of DIS 2007

## Chiral-Odd Generalized Parton Distributions from Exclusive pi^o Electroproduction

Liuti, Simonetta; Goldstein, Gary R.; Ahmad, Saeed
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.19%
Exclusive $\pi^o$ electroproduction is suggested for extracting both the tensor charge and the transverse anomalous magnetic moment from experimental data. A connection between partonic degrees of freedom, given in terms of Generalized Parton Distributions, and Regge phenomenology is discussed. Calculations are performed using a physically motivated parametrization that is valid at values of the skewness, $\zeta \neq 0$. Our method makes use of information from the nucleon form factor data, from deep inelastuc scattering parton distribution functions, and from lattice results on the Mellin moments of generalized parton distributions. It provides, therefore, a step towards a model independent extraction of generalized distributions from the data, alternative to other mathematical ansatze available in the literature.; Comment: 4 pages, Proceedings of DIS 2008, 7-11 April 2008, University College London

## Generalized Non-extensive Statistical Distributions

Sotolongo-Costa, Oscar; Gonzalez, Alejandro Gonzalez; Brouers, Francois
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.21%
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using the Tsallis' and Renyi information measures instead of the well-known Bolztmann-Gibbs-Shannon. These generalized distributions will depend on q (real number) and in the limit (q=1) we obtain the "classical" ones. We found that apart from a constant, generalized versions of statistical distributions following Tsallis' or Renyi are undistinguishable.; Comment: 11 pages, to be submitted for publication

## The new class of Kummer beta generalized distributions

Pescim, R. R.; Cordeiro, G. M.; Demétrio, C. G. B.; Ortega, E. M. M.; Nadarajah, S.
Tipo: Artigo de Revista Científica Formato: application/pdf