Four generalized Weibull distributions: similar properties and applications

We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation

The Complementary Extended Weibull Power Series Class of Distributions

http://dx.doi.org/10.5902/2179460X13194Neste artigo, introduzimos um método geral para obter distribuições de probabilidade mais flexíveis por meio da composição dasclasses Weibull estendida e da séries de potência no contexto de riscos competitivos. As propriedades da nova classe são descritas,incluindo uma prova formal para a expansão da função densidade e fórmulas explícitas para a função taxa de risco, quantils,momentos ordinários e incompletos e função geradora. O método de máxima verossimilhança é usada para estimar os parâmetrosdo modelo. Algumas distribuições especiais são estudadas. A potencialidade da nova classe é ilustrada com uma aplicação a umconjunto de dados reais.Neste artigo, introduzimos um método geral para obter novas distribuições mais flexíveis, compondo as distribuições estendidas de séries de potência Weibulland em uma base latente de problemas de risco complementares. As propriedades da classe proposta são discutidas, incluindo uma prova formal de uma expensão para sua função de densidade e fórmulas explícitas para sua função de taxa de risco, quantis, momentos ordinários e incompletos e função geradora. O método de máxima verossimilhança é usado para estimar os parâmetros do modelo. Distribuições especiais são investigadas. A potencialidade da nova classe é ilustrada em um conjunto de dados real

Como evoluíram os níveis de estresse e ansiedade em docentes e discentes universitários durante a pandemia da COVID-19?- um estudo transversal repetido / How did stress and anxiety levels evolve in university professors and students during the COVID-19 pandemic? - a repeated cross-sectional study

O objetivo deste artigo é estudar de forma comparativa a evolução dos níveis de estresse e ansiedade em estudantes e professores universitários durante a pandemia da COVID-19. O método utilizado foi de um estudo transversal repetido três vezes, após o término de cada semestre letivo, com uma amostra de docentes e discentes dos cursos de bacharelado da área de exatas da UFPE.  Os instrumentos utilizados foram: um formulário de coleta de dados sociodemográficos, econômicos e de opinião sobre o ensino remoto. A saúde mental foi avaliada pela Escala de Ansiedade, Estresse e Depressão-21 (DASS-21). Os resultados mostram que a prevalência dos sintomas de estresse são maiores que os de ansiedade tanto em docentes quanto em discentes, ao longo do período analisado. Os mesmos sugerem ainda um impacto psicológico negativo da pandemia maior nos estudantes que nos professores

MODELAGEM DO CRESCIMENTO DE CLONES DE Eucalyptus USANDO O MODELO DE CHAPMAN-RICHARDS COM DIFERENTES DISTRIBUI\uc7 5ES SIM\uc9TRICAS DOS ERROS

The objective of this work was to estimate the height growth of Eucalyptus using the Chapman-Richards model considering for the errors the distributions normal, Student t (t) and Cauchy. The data set came from one hybrid clone of Eucalyptus urophylla x Eucalyptus tereticornis x Eucalyptus pellita (controlled pollination), of the Forestry Experimental Module in the Gypsum Pole of Araripe, established in 2002. Eighty-three trees were used which heights were measured in all trees for six and half years. The parameters of the Chapman- Richards model were obtained maximizing the log-likelihood function. For comparison of the adjusted models were used the criteria of Akaike Information Criterion (AIC) and Bayesian (BIC) and the mean absolute percentage error (MAPE). The model using the t distribution with 2 degrees of freedom (t2) had lower values of AIC and BIC and the model of Cauchy had lower value for MAPE. The results indicate that the model considering the t distribution for the errors presented best estimates of height growth of Eucalyptus hybrid clones in Gypsum Pole of Pernambuco.Objetivou-se neste trabalho estimar o crescimento em altura de clones de Eucalyptus usando o modelo de Chapman-Richards, considerando para os erros as distribui\ue7\uf5es: normal, t de Student (t) e Cauchy. Foram utilizados dados de clones de h\uedbrido entre Eucalyptus urophylla x Eucalyptus tereticornis x Eucalyptus pellita (poliniza\ue7\ue3o controlada), do M\uf3dulo de Experimenta\ue7\ue3o Florestal para o Polo Gesseiro do Araripe, implantado em 2002. Utilizaram-se 83 \ue1rvores cujas alturas foram medidas durante seis anos e meio. Os par\ue2metros do modelo de Chapman-Richards foram obtidos maximizando a fun\ue7\ue3o de log-verossimilhan\ue7a. Para compara\ue7\ue3o dos modelos foram utilizados os crit\ue9rios de informa\ue7\ue3o de Akaike (CIA) e Bayesiana (CIB) e o erro percentual absoluto m\ue9dio (EPAM). O modelo usando a distribui\ue7\ue3o t de Student com 2 graus de liberdade (t2) obteve menores valores de CIA e CIB enquanto que o modelo de Cauchy obteve menor valor para o EPAM. Os resultados indicam que o modelo, considerando distribui\ue7\ue3o t para os erros, apresentou melhores estimativas do crescimento em altura de clones h\uedbrido de Eucalyptus no Polo Gesseiro de Pernambuco

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals

On the burr XII-gamma distribution: development, properties, characterizations and applications

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution. We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations. We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model

The Zeta-G Class: Some Computational and Analytical Aspects

We define a new class of distributions with one extra shapeparameter including some special cases. We provide numerical and computational aspects of the new class. We proposefunctions using the \textsf{R} language to fit any distribution in this family to a data set. In addition, such functions are implemented efficientlyusing the library \textsf{Rcpp} that enables the incorporation of the codes \textsf{C++} in \textsf{R} automatically. Some examples are presentedfor using the implemented routines in practice. We derive some mathematical properties of this class including explicit expressionsfor the moments, generating function and mean deviations. We discuss the estimation of the model parametersby maximum likelihood and provide an application to a real data set

A power series beta Weibull regression model for predicting breast carcinoma

The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had adisease, but they do not accurately predict what will happen in any particular patient’s case. Pathologic explana-tory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion, and enhancedlymph node staining are prognostically signicant to predict these survival rates. We propose a new cure ratesurvival regression model for predicting breast carcinoma survival in women who underwent mastectomy. Weassume that the unknown number of competing causes that can inuence the survival time is given by a powerseries distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows thebeta Weibull distribution. The new compounding regression model includes as special cases several well-knowncure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Fur-ther, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed.We derive the appropriate matrices for assessing local inuences on the parameter estimates under different per-turbation schemes and present some ways to assess local inuences. The potentiality of the new regression modelto predict accurately breast carcinoma mortality is illustrated by means of real data. Copyright © 2015 JohnWiley & Sons, Ltd