The exponentiated generalized gamma distribution with application to lifetime data

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.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several 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 define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Introduction

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Mammalia

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Aves. v. 1. Introduction -- Subclass Aves Carinate. Order Passeres.

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Aves. v. 2. Subclass Aves Carinate. Order[s]: Passeres (contd.), Macrochires, Pici, Coccyges, Psitta

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Aves. v. 3. Subclass Aves Carinate. Order[s]: Striges, Accipitres, Steganopodes, Phoenicopteri, Colu

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Aves. v. 4. Plates.

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Reptilia and Batrachia

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Pisces

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Land and Freshwater Mollusca

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Arachnida Araneidea

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Arachnida Araneidea and Opiliones

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Arachnida, Scorpiones, Pedipalpi, and Solifugae

Biologia Centrali-Americana :zoology, botany and archaeology /edited by Frederick Ducane Godman and Osbert Salvin.

Chilopoda and Diplopoda