The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

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.

Isolation and characterization of actinobacteria ectosymbionts from Acromyrmex subterraneus brunneus (Hymenoptera, Formicidae)

The ectosymbiont actinobacterium Pseudonocardia was isolated from the integument of Acromyrmex leaf-cutter ants and seems to play a crucial role in maintaining asepsis of the nest. Currently, there has been an intensive search for Pseudonocardia associated with several attine species, but few studies have indicated that other actinobacteria may be associated with these ants as well. We therefore characterized the culturable actinobacteria community associated with the integument of the fungus-growing ant Acromyrmex subterraneus brunneus Forel, 1893 (Hymenoptera: Formicidae). Ectosymbionts were isolated using four different media and characterized by morphological and molecular (16S rDNA) methods. A total of 20 strains were isolated, of which 17 were characterized as Streptomyces spp., and one isolate each as Pseudonocardia, Kitassatospora and Propionicimonas. Unlike other Acromyrmex species, A. subterraneus brunneus is associated with a diversity of actinobacteria. Even though Pseudonocardia is present on this leaf-cutting ant`s integument, the number and diversity of Streptomyces spp. found differs from those of previous studies with other attine ants and suggest that different culturing approaches are needed to characterize the true diversity of microbes colonizing the integument of attine ants. Moreover, understanding the diversity of the culturable actinobacteria associated with A. subterraneus brunneus should increase our knowledge of the evolutionary relationship of this intricate symbiotic association. (C) 2010 Elsevier GmbH. All rights reserved.

Positive selection on an acrosomal sperm protein, M7 lysin, in three species of the mussel genus Mytilus

Marine invertebrate sperm proteins are particularly interesting because they are characterized by positive selection and are likely to be involved in prezyogotic isolation and, thus, speciation. Here, we present the first survey of inter and intraspecific variation of a bivalve sperm protein among a group of species that regularly hybridize in nature. M7 lysin is found in sperm acrosomes of mussels and dissolves the egg vitelline coat, permitting fertilization. We sequenced multiple alleles of the mature protein-coding region of M7 lysin from allopatric populations of mussels in the Mytilus edulis species group (M. edulis, M. galloprovincialis, and M. trossulus). A significant McDonald-Kreitman test showed an excess of fixed amino acid replacing substitutions between species, consistent with positive selection. In addition, Kolmogorov-Smirnov tests showed significant heterogeneity in polymorphism to divergence ratios for both synonymous variation and combined synonymous and non-synonymous variation within M. galloprovincialis. These results indicate that there has been adaptive evolution at M7 lysin and, furthermore, shows that positive selection on sperm proteins can occur even when post-zygotic reproductive isolation is incomplete.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Distinguishing species and populations of Rhipicephaline ticks with its 2 ribosomal RNA

Most populations and some species of ticks of the genera Boophilus (5 spp.) and Rhipicephalus (ca. 75 spp.) cannot be distinguished phenotypically. Moreover, there is doubt about the validity of species in these genera. I studied the entire second internal transcribed spacer (ITS 2) rRNA of 16 populations of rhipicephaline ticks to address these problems: Boophilus,microplus from Australia, Kenya, South Africa and Brazil (4 populations); Boophilus decoloratus from Kenya; Rhipicephalus appendiculatus from Kenya, Zimbabwe and Zambia (7 populations); Rhipicephalus zambesiensis from Zimbabwe (3 populations); and Rhipicephalus evertsi from Kenya. Each of the 16 populations had a unique ITS 2, but most of the nucleotide variation occurred among species and genera. ITS 2 rRNA can be used to distinguish the populations and species of Boophilus and Rhipicephalus studied here. Little support was found for the hypothesis that B. microplus from Australia and South Africa are different species. ITS 2 appears useful for phylogenetic inference in the Rhipicephalinae because in genetic distance, maximum likelihood, and maximum parsimony analyses, most branches leading to species had >95% bootstrap support. Rhipicephalus appendiculatus and R, zambeziensis are closely related, yet their ITS 2 sequences could be distinguished unambiguously. This lends weight to a previous proposal that Rhipicephalus sanguineus and Rhipicephalus turanicus, and Rhipicephalus pumlilio and Rhipicephalus camicasi, respectively, are conspecific, because each of these pairs of species had identical sequences for ca. 250 bp of ITS 2 rRNA.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

Hemichordates and deuterostome evolution: robust molecular phylogenetic support for a hemichordate plus echinoderm clade

Hemichordates were traditionally allied to the chordates, but recent molecular analyses have suggested that hemichordates are a sister group to the echinoderms, a relationship that has important consequences for the interpretation of the evolution of deuterostome body plans. However, the molecular phylogenetic analyses to date have not provided robust support for the hemichordate + echinoderm clade. We use a maximum likelihood framework, including the parametric bootstrap, to reanalyze DNA data from complete mitochondrial genomes and nuclear 18S rRNA. This approach provides the first statistically significant support for the hemichordate + echinoderm clade from molecular data. This grouping implies that the ancestral deuterostome had features that included an adult with a pharynx and a dorsal nerve cord and an indirectly developing dipleurula-like larva.