Cibele Q. da-Silva

The beta exponentiated Weibull distribution

The Weibull distribution is one of the most important distributions in reliability. For the first time, we introduce the beta exponentiated Weibull distribution which extends recent models by Lee et al. [Beta-Weibull distribution: some properties and applications to censored data, J. Mod. Appl. Statist. Meth. 6 (2007), pp. 173–186] and Barreto-Souza et al. [The beta generalized exponential distribution, J. Statist. Comput. Simul. 80 (2010), pp. 159–172]. The new distribution is an important competitive model to the Weibull, exponentiated exponential, exponentiated Weibull, beta exponential and beta Weibull distributions since it contains all these models as special cases. We demonstrate that the density of the new distribution can be expressed as a linear combination of Weibull densities. We provide the moments and two closed-form expressions for the moment-generating function. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The density of the order statistics can also be expressed as a linear combination of Weibull densities. We obtain the moments of the order statistics. The expected information matrix is derived. We define a log-beta exponentiated Weibull regression model to analyse censored data. The estimation of the parameters is approached by the method of maximum likelihood. The usefulness of the new distribution to analyse positive data is illustrated in two real data sets.

Seasonality in reproduction, age structure and density of the gracile mouse opossum Gracilinanus microtarsus (Marsupialia: Didelphidae) in a Brazilian cerrado

The temporal pattern of reproduction and its consequences for age structure and density were investigated in a population of the gracile mouse opossum Gracilinanus microtarsus in south-eastern Brazil. Individuals of G. microtarsus were monitored through capture-mark-recapture methods from August 2000 to February 2003 in a remnant of cerradao, a forest-like physiognomy of the highly seasonal cerrado biome. The temporal pattern of reproduction of the population studied was highly seasonal with rearing of the offspring occurring in the first half of the warm-wet season, when the abundance of food resources primarily insects in the cerrado is high. Shortly after reproduction, the density of adults decreased sharply, possibly because of high post-mating mortality, leading to a gradual replacement of adults by their offspring in the following months and little overlap of generations. Our data suggest that climatic and environmental factors affect the onset of reproduction and interact with endogenous factors that decrease post-mating survival to produce the observed pattern of seasonal variation in age structure and density. It is suggested that the dynamics of populations of G. microtarsus may be driven primarily by food limitation and that long-term studies are needed to understand its feedback structure.

PARTIAL SEMELPARITY IN THE NEOTROPICAL DIDELPHID MARSUPIAL GRACILINANUS MICROTARSUS

Abstract Semelparity has been demonstrated in males of several species of Australian dasyurid marsupials. Although semelparity also has been reported in some species of neotropical didelphid marsupials, no study has conclusively demonstrated its occurrence based on survival rate estimates from field studies of marked individuals. In this study, we demonstrate that the survival rates of males of a Neotropical didelphid marsupial, the Brazilian gracile mouse opossum (Gracilinanus microtarsus), decrease sharply after the beginning of the breeding season in a cerrado remnant. However, mortality of the males after mating is not complete and a small percentage of them may survive to breed again in a 2nd breeding season. Examination of the demographic data presented here conclusively demonstrates that G. microtarsus is best described as partially semelparous.

Dynamic Bayesian beta models

We develop a dynamic Bayesian beta model for modeling and forecasting single time series of rates or proportions. This work is related to a class of dynamic generalized linear models (DGLMs), although, for convenience, we use non-conjugate priors. The proposed methodology is based on approximate analysis relying on Bayesian linear estimation, nonlinear system of equations solution and Gaussian quadrature. Intentionally we avoid MCMC strategy, keeping the desired sequential nature of the Bayesian analysis. Applications to both real and simulated data are provided.

Ecology of the Armadillos Cabassous unicinctus and Euphractus sexcinctus (Cingulata: Dasypodidae) in a Brazilian Cerrado

Abstract We report on aspects of the ecology and natural history of 2 species of armadillos commonly found in a cerrado remnant in southeastern Brazil—the naked-tailed armadillo (Cabassous unicinctus) and the 6-banded armadillo (Euphractus sexcinctus). Armadillos were captured in pitfall traps or by hand, double-marked, and the habitat (campo sujo, campo cerrado, and gallery forests), season, and time of capture were recorded. We also recorded the sex and age of all armadillos, and reproductive condition of females. Population densities were estimated as 0.27 and 0.14 individuals/ha for C. unicinctus and E. sexcinctus, respectively. E. sexcinctus did not preferentially use any of the habitats included in the study area, whereas C. unicinctus preferentially used habitats with a more complex vegetation structure, such as gallery forests. C. unicinctus was diurnal and E. sexcinctus was mainly nocturnal. Neither species changed its activity pattern with season, but C. unicinctus was more active in months with decreased abundance of arthropods—the main food resource consumed by this species. Both species of armadillos appeared to reproduce year-round. Differences in habitat use and daily activity between C. unicinctus and E. sexcinctus suggest spatial and temporal displacement between these species.

A new lifetime model: the Kumaraswamy generalized Rayleigh distribution

The generalized Rayleigh (GR) distribution [V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, I, Appl. Math. 21 (1976), pp. 395–412; V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, II, Appl. Math. 21 (1976), pp. 413–419] has been applied in several areas such as health, agriculture, biology and other sciences. For the first time, we propose the Kumaraswamy GR (KwGR) distribution for analysing lifetime data. The new density function can be expressed as a mixture of GR density functions. Explicit formulae are derived for some of its statistical quantities. The density function of the order statistics can be expressed as a mixture of GR density functions. We also propose a linear log-KwGR regression model for analysing data with real support to extend some known regression models. The estimation of parameters is approached by maximum likelihood. The importance of the new models is illustrated in two real data sets.

A spatial scan statistic for zero-inflated Poisson process

The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to data with excess zeros, the spatial scan statistic may produce biased inferences. In this work, we develop a closed-form scan statistic for cluster detection of spatial zero-inflated count data. We apply our methodology to simulated and real data. Our simulations revealed that the Scan-Poisson statistic steadily deteriorates as the number of zeros increases, producing biased inferences. On the other hand, our proposed Scan-ZIP and Scan-ZIP+EM statistics are, most of the time, either superior or comparable to the Scan-Poisson statistic.

A Confirmatory Factor Analysis Approach to Test Anxiety

This article addresses the role of test anxiety in aptitude testing. Our approach is rooted in confirmatory factor analysis (CFA). We find that the usual parameter constraints used for model identification in CFA have nontrivial implications for the effects of interest. We suggest 2 methods for dealing with this identification problem. First, we consider testable parameter constraints that identify the proposed model. Second, we consider structural relations that do not depend on model identification. In particular we derive the partial factor correlation between a test and an external variable, conditional on test anxiety, and show that this correlation (a) is not affected by the choice of model identification constraints, and (b) can be estimated using true score theory.

Two Extended Burr Models: Theory and Practice

We propose two new six-parameter distributions, called the McDonald Burr III and McDonald Burr XII models, which contain some recently published distributions as special models. We provide a comprehensive description of some of their mathematical properties with the hope that they will attract wider applications in lifetime analysis. The potentiality of both models to analyze positive data is illustrated by means of two real data sets.

Another extended Burr III model: some properties and applications

We introduce an extended Burr III distribution as an important model for problems in survival analysis and reliability. The new distribution can be expressed as a linear combination of Burr III distributions and then it has tractable properties for the ordinary and incomplete moments, generating and quantile functions, mean deviations and reliability. The density of its order statistics can be given in terms of an infinite linear combination of Burr III densities. The estimation of the model parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed model is applied to a real data set to illustrate its potentiality.