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## The exponentiated generalized gamma distribution with application to lifetime data

CORDEIRO, Gauss M.; ORTEGA, Edwin M. M.; SILVA, Giovana O.
Fonte: TAYLOR & FRANCIS LTD Publicador: TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
55.99%
A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.; CAPES; CNPq

## Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

Barajas, Freddy Hernandez; USUGA, Olga Cecilia
Tipo: Artigo de Revista Científica
SPA
Relevância na Pesquisa
55.93%
There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

## Robust modeling using the generalized epsilon-skew-t distribution

Venegas, Osvaldo; Rodriguez, Francisco; Gomez, Hector W.; Olivares-Pacheco, Juan F.; Bolfarine, Heleno
Fonte: TAYLOR & FRANCIS LTD; ABINGDON Publicador: TAYLOR & FRANCIS LTD; ABINGDON
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
45.97%
In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.; DGIP (Chile); DGIP (Chile) [200921]; UBB (Chile) [0905232I]; UBB (Chile); CNPq (Brasil); CNPq (Brasil); FONDECYT (Chile) [1090411]; FONDECYT (Chile)

## The McDonald extended distribution: properties and applications

Cordeiro, Gauss M.; Hashimoto, Elizabeth M.; Ortega, Edwin M. M.; Pascoa, Marcelino A. R.
Fonte: SPRINGER; NEW YORK Publicador: SPRINGER; NEW YORK
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.15%
We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.; FAPESP; FAPESP [2010/04496-2]; CNPq, Brazil; CNPq (Brazil)

Couto, Epaminondas de Vasconcellos
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
56.14%

## 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
96.08%

## 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
96.25%
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.

## How to deal with extreme observations in empirical finance: an application to capital markets

Silva, Josué de Sousa e
Fonte: Instituto Universitário de Lisboa Publicador: Instituto Universitário de Lisboa
Relevância na Pesquisa
45.98%
Mestrado em Finanças; In the last few years, Extreme Value Theory (EVT) has gained increased importance in modeling extreme observations in all social sciences. This is especially true in finance, since EVT is a tool used to consider probabilities associated with extreme and rare events with catastrophic consequences, as happened in the Sub-prime crisis in 2007. To model extreme observations, we use two different statistical distribution families in this thesis: Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD). In this thesis, EVT methods were used to investigate and fit the empirical distribution of the monthly maximum and minimum return series of the FTSE 100, NIKKEI 225 and S&P500 indices to the theoretical GEV and GPD distributions. We have applied two approaches of extreme value theory, the Block Maxima and the Peaks Over Threshold (POT) approach, as well as the parametric approach of the Maximum Likelihood Estimate Method (MLE) for the distribution parameter estimation and the non-parametric approach of the Hill estimator. As a result of the application, we have seen that in the GEV distribution application, our data was well represented by the Fréchet and Weibull distributions. On the other hand...

## A BIVARIATE GENERALIZED EXPONENTIAL DISTRIBUTION DERIVED FROM COPULA FUNCTIONS IN THE PRESENCE OF CENSORED DATA AND COVARIATES

Achcar,Jorge Alberto; Moala,Fernando Antônio; Tarumoto,Mario Hissamitsu; Coladello,Leandro Fernandes
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
96.13%
In this paper, we introduce a Bayesian analysis for a bivariate generalized exponential distribution in the presence of censored data and covariates derived from Copula functions. The generalized exponential distribution could be a good alternative to analyze lifetime data in comparison to usual existing parametric lifetime distributions as Weibull or Gamma distributions. We have being using standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest. Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate lifetime data and an example with a real lifetime data set.

## The Beta Generalized Exponential Distribution

Barreto-Souza, Wagner; Santos, Alessandro H. S.; Cordeiro, Gauss M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.15%
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions.

## Ordering Properties of Order Statistics from Heterogeneous Generalized Exponential and Gamma Populations

Kundu, Amarjit; Chowdhury, Shovan; Nanda, Asok K.; Hazra, Nil Kamal
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.02%
Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp. $\delta_i$), $i=1,2,\ldots, n$. Here it is shown that if $\left(\lambda_1, \lambda_2,\ldots,\lambda_n\right)$ is $p$-larger than (resp. weakly supermajorizes) $\left(\delta_1,\delta_2,\ldots,\delta_n\right)$, then $X_{n:n}$ will be greater than $Y_{n:n}$ in usual stochastic order (resp. reversed hazard rate order). That no relation exists between $X_{n:n}$ and $Y_{n:n}$, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if $Y_i$ follows generalized exponential distribution with parameters $\left(\overline\lambda,\theta_i\right)$, where $\overline\lambda$ is the mean of all $\lambda_i$'s, $i=1\ldots n$, then $X_{n:n}$ is greater than $Y_{n:n}$ in likelihood ratio ordering. Some new results on majorization have been developed which fill up some gap in the theory of majorization. Some results on multiple-outlier model are also discussed. In addition to this, we compare two series systems formed by gamma components with respect to different stochastic orders.

## The Odd Generalized Exponential Gompertz

El-Damcese, M. A.; Mustafa, Abdelfattah; El-Desouky, B. S.; Mustafa, M. E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.92%
In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood method is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.; Comment: 14 Pages, 7 figures(11 Images), 3 Tables

## Modeling of magnitude distributions by the generalized truncated exponential distribution

Raschke, Mathias
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.17%
The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cut-off exponential distribution (CED). The TED is frequently used in seismic hazard analysis although it has a weak point: When two TEDs with equal parameters except the upper bound magnitude are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of sub-regions with equal parameters except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. We overcome it by the generalization of the above-mentioned exponential distributions: the generalized truncated exponential distribution (GTED). Therein, identical exponential distributions are mixed by the probability distribution of the correct cut-off points. This distribution model is flexible in the vicinity of the upper bound magnitude and is equal to the exponential distribution for smaller magnitudes. Additionally, the exponential distributions TED and CED are special cases of the GTED. We discuss the possible ways of estimating its parameters and introduce the normalized spacing for this purpose. Furthermore...

## Estimators for the Parameter Mean of Morgenstern Type Bivariate Generalized Exponential Distribution Using Ranked Set Sampling

Tahmasebi, Saeid; Jafari, Ali Akbar
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.95%
In situations where the sampling units in a study can be more easily ranked based on the measurement of an auxiliary variable, ranked set sampling provide unbiased estimators for the mean of a population that they are more efficient than unbiased estimator based on simple random sample. In this paper, we consider the Morgenstern type bivariate generalized exponential distribution (MTBGED) and obtain several unbiased estimators for a parameter mean of the marginal distribution of MTBGED based on different ranked set sampling schemes. The efficiency of all considered estimators are evaluate and has also been demonstrated with numerical illustrations.; Comment: Accepted for publication SORT - Statistics and Operations Research Transactions; 2014

## Generalized Exponential Function and some of its Applications to Complex Systems

Martinez, Alexandre Souto; Gonzalez, Rodrigo Silva; Tercariol, Cesar Augusto Sangaletti
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.07%
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing complex systems can be conveniently written in terms of this generalization of the exponential function. The gamma function is then generalized and we generalize the factorial operation. Also a very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. One obtains, as particular cases, the generalized error function, the Zipf-Mandelbrot probability density function (pdf), the generalized gaussian and Laplace pdf. One can also obtain analytically their cumulative functions and moments.; Comment: 16 pages and 2 figures

## The generalized lognormal distribution and the Stieltjes moment problem

Kleiber, Christian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.98%
This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential of a random variable following a generalized error distribution, and hence figures prominently in the EGARCH model of asset price volatility. Compared to the classical lognormal distribution it has an additional shape parameter. It emerges that moment (in)determinacy depends on the value of this parameter: for some values, the distribution does not have finite moments of all orders, hence the moment problem is not of interest in these cases. For other values, the distribution has moments of all orders, yet it is moment-indeterminate. Finally, a limiting case is supported on a bounded interval, and hence determined by its moments. For those generalized lognormal distributions that are moment-indeterminate Stieltjes classes of moment-equivalent distributions are presented.; Comment: 12 pages, 1 figure

## On Bivariate Generalized Exponential-Power Series Class of Distributions

Jafari, Ali Akbar; Roozegar, Rasool
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.02%
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties of the new class of distributions. The EM algorithm is used to determine the maximum likelihood estimates of the parameters. We illustrate the usefulness of the new distributions by means of an application to a real data set.; Comment: arXiv admin note: text overlap with arXiv:1507.07535

## The Odd Generalized Exponential Linear Failure Rate Distribution

El-Damcese, M. A.; Mustafa, Abdelfattah; El-Desouky, B. S.; Mustafa, M. E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.97%
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode are investigated. The method of maximum likelihood is used for estimating the model parameters. An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.; Comment: 15 Pages, 9 Figures (15 Images), 3 Tables. arXiv admin note: text overlap with arXiv:1507.06400

## Estimators for the parameter mean of Morgenstern type bivariate generalized exponential distribution using ranked set sampling

Tahmasebi, Saeid; Akbar Jafari, Ali
Tipo: Artigo de Revista Científica Formato: application/pdf