New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models

Influence diagnostics in exponentiated-Weibull regression models with censored data.

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from the error assumptions and the presence of outliers and influential observations with the fitted models. The literature provides plenty of approaches for detecting outlying or influential observations in data sets. In this paper, we follow the local influence approach (Cook 1986) in detecting influential observations with exponentiated-Weibull regression models. The relevance of the approach is illustrated with a real data set, where it is shown that by removing the most influential observations, there is a change in the decision about which model fits the data better.Peer Reviewe

Influence diagnostics in exponentiated-Weibull regression models with censored data

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from the error assumptions and the presence of outliers and influential observations with the fitted models. The literature provides plenty of approaches for detecting outlying or influential observations in data sets. In this paper, we follow the local influence approach (Cook 1986) in detecting influential observations with exponentiated-Weibull regression models. The relevance of the approach is illustrated with a real data set, where it is shown that by removing the most influential observations, there is a change in the decision about which model fits the data better

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.32211513

A new extended mixture normal distribution

The normal distribution is the most important model in statistics for analysis of continuous data. We propose a new distribution, called the extended mixture normal distribution, based on a linear mixture model. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations and two measures of entropy. The maximum likelihood and Bayesian methods are used to estimate the model parameters. We prove empirically that the new distribution can be a better model than the normal and other classical distributions by means of an application to real data

Assessing influence in survival data with a cure

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed

Relação entre uso do solo e composição de insetos aquáticos de quatro bacias hidrográficas do Estado de São Paulo

Four watersheds with different degrees of human occupation had their communities of aquatic insects analyzed in relation to the landuses, terrain slope as well as chemical and physical variables of water. The watersheds studied were Alto Paranapanema, Peixe, Aguapei and São José dos Dourados. Samples of aquatic insects were taken with baskets filled with artificial substrates, during August and October/2002. Eighteen samples were taken from eachriver and the aquatic insects were identified until family level and counted. To analyze the results, total and percentage numbers of individuals and taxons were used, as well as community indeces. Information about the watersheds were generated from digital maps. Thirty-two families were identified, Elmidae, Leptohyphidae, Leptophlebiidae, Chironomidae, Simuliidae and Hydropsychidae showed numeric dominance. Ten chemical and physical variablestested were able to characterize the rivers; percentages of the main landuses and terrain slope were calculated. Pearson’s correlation index, analysis of variance and analysis of correspondence were used in order to establish the relationship between abiotic components and the entomofauna. The study showed that the land use condition immediately adjacent tothe sampling site is the most important factor influencing that fauna.Key words: aquatic macroinvertebrates, lotic environments, riparian forest, rivers, Southern.As comunidades de insetos aquáticos de quatro bacias hidrográficas sob diferentes graus de ocupação humana foram analisadas em relação aos usos do solo, à declividade do terreno e às variáveis físicas e químicas da água. As bacias hidrográficas estudadas foram Alto Paranapanema, Peixe, Aguapeí e São José dos Dourados. Amostras de insetos aquáticos foram coletadas utilizando-se cestos com substrato artificial, entre agosto e outubro de 2002. Foram colocadas 18 repetições em cada rio, e os insetos amostrados foram identificados em nível de família e contados. Os dados foram analisados em números absolutos e percentuais de indivíduos e de táxons, e também índices comunitários. Informações sobre as bacias hidrográficas foram geradas a partir de mapas digitais. Foram identificadas 32 famílias, Elmidae, Leptohyphidae, Leptophlebiidae, Chironomidae, Simuliidae e Hydropsychidae apresentaram dominância. Dez variáveis físicas e químicas da água apresentaram relação direta sobre os rios; porcentagens dos usos do solo e das declividades foram calculadas. Utilizou-se a correlação de Pearson, Análise de Variância (ANOVA) e análise de correspondência para integraros dados abióticos e biológicos. O estudo mostrou a importância do uso do solo imediatamente adjacente ao local de coleta como o fator de maior influência sobre a entomo fauna.Palavras-chave: ambientes lóticos, macroinvertebrados aquáticos, rios, sudeste do Brasil, vegetação ripária

A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications

Abstract We define two new flexible families of continuous distributions to fit real data by compoun-ding the Marshall–Olkin class and the power series distribution. These families are very competitive to the popular beta and Kumaraswamy generators. Their densities have linear representations of exponentiated densities. In fact, as the main properties of thirty five exponentiated distributions are well-known, we can easily obtain several properties of about three hundred fifty distributions using the references of this article and five special cases of the power series distribution. We provide a package implemented in R software that shows numerically the precision of one of the linear representations. This package is useful to calculate numerical values for some statistical measurements of the generated distributions. We estimate the parameters by maximum likelihood. We define a regression based on one of the two families. The usefulness of a generated distribution and the associated regression is proved empirically