The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

BENTHIC MACROFAUNA STRUCTURE IN THE NORTHEAST AREA OF TODOS OS SANTOS BAY, BAHIA STATE, BRAZIL: PATTERNS OF SPATIAL AND SEASONAL DISTRIBUTION

Structure of intertidal and subtidal benthic macrofauna in the northeastern region of Todos os Santos Bay (TSB), northeast Brazil, was investigated during a period of two years. Relationships with environmental parameters were studied through uni- and multivariate statistical analyses, and the main distributional patterns shown to be especially related to sediment type and content of organic fractions (Carbon, Nitrogen, Phosphorus), on both temporal and spatial scales. Polychaete annelids accounted for more than 70% of the total fauna and showed low densities, species richness and diversity, except for the area situated on the reef banks. These banks constitute a peculiar environment in relation to the rest of the region by having coarse sediments poor in organic matter and rich in biodetritic carbonates besides an abundant and diverse fauna. The intertidal region and the shallower area nearer to the oil refinery RLAM, with sediments composed mainly of fine sand, seem to constitute an unstable system with few highly dominant species, such as Armandia polyophthalma and Laeonereis acuta. In the other regions of TSB, where muddy bottoms predominated, densities and diversity were low, especially in the stations near the refinery. Here the lowest values of the biological indicators occurred together with the highest organic compound content. In addition, the nearest sites (stations 4 and 7) were sometimes azoic. The adjacent Caboto, considered as a control area at first, presented low density but intermediate values of species diversity, which indicates a less disturbed environment in relation to the pelitic infralittoral in front of the refinery. The results of the ordination analyses evidenced five homogeneous groups of stations (intertidal; reef banks; pelitic infralittoral; mixed sediments; Caboto) with different specific patterns, a fact which seems to be mainly related to granulometry and chemical sediment characteristics.

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

An extension of the half-normal distribution

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.

Global pharmacogenomics: Impact of population diversity on the distribution of polymorphisms in the CYP2C cluster among Brazilians

The impact of biogeographical ancestry, self-reported 'race/color' and geographical origin on the frequency distribution of 10 CYP2C functional polymorphisms (CYP2C8*2, *3, *4, CYP2C9*2, *3, *5, *11, CYP2C19*2, *3 and *17) and their haplotypes was assessed in a representative cohort of the Brazilian population (n = 1034). TaqMan assays were used for allele discrimination at each CYP2C locus investigated. Individual proportions of European, African and Amerindian biogeographical ancestry were estimated using a panel of insertion-deletion polymorphisms. Multinomial log-linear models were applied to infer the statistical association between the CYP2C alleles and haplotypes (response variables), and biogeographical ancestry, self-reported Color and geographical origin (explanatory variables). The results showed that CYP2C19*3, CYP2C9*5 and CYP2C9*11 were rare alleles (<1%), the frequency of other variants ranged from 3.4% (CYP2C8*4) to 17.3% (CYP2C19*17). Two distinct haplotype blocks were identified: block 1 consists of three single nucleotide polymorphisms (SNPs) (CYP2C19*17, CYP2C19*2 and CYP2C9*2) and block 2 of six SNPs (CYP2C9*11, CYP2C9*3, CYP2C9*5, CYP2C8*2, CYP2C8*4 and CYP2C8*3). Diplotype analysis generated 41 haplotypes, of which eight had frequencies greater than 1% and together accounted for 96.4% of the overall genetic diversity. The distribution of CYP2C8 and CYP2C9 (but not CYP2C19) alleles, and of CYP2C haplotypes was significantly associated with self-reported Color and with the individual proportions of European and African genetic ancestry, irrespective of Color self-identification. The individual odds of having alleles CYP2C8*2, CYP2C8*3, CYP2C9*2 and CYP2C9*3, and haplotypes including these alleles, varied continuously as the proportion of European ancestry increased. Collectively, these data strongly suggest that the intrinsic heterogeneity of the Brazilian population must be acknowledged in the design and interpretation of pharmacogenomic studies of the CYP2C cluster in order to avoid spurious conclusions based on improper matching of study cohorts. This conclusion extends to other polymorphic pharmacogenes among Brazilians, and most likely to other admixed populations of the Americas. The Pharmacogenomics Journal (2012) 12, 267-276; doi: 10.1038/tpj.2010.89; published online 21 December 2010

Spatial distribution of arboviral mosquito vectors (Diptera, Culicidae) in Vale do Ribeira in the South-eastern Brazilian Atlantic Forest

Mosquitoes are vectors of arboviruses that can cause encephalitis and hemorrhagic fevers in humans. Aedes serratus (Theobald), Aedes scapularis (Rondani) and Psorophora ferox (Von Humboldt) are potential vectors of arboviruses and are abundant in Vale do Ribeira, located in the Atlantic Forest in the southeast of the State of Sao Paulo, Brazil. The objective of this study was to predict the spatial distribution of these mosquitoes and estimate the risk of human exposure to mosquito bites. Results of the analyses show that humans are highly exposed to bites in the municipalities of Cananeia, Iguape and Ilha Comprida. In these localities the incidence of Rocio encephalitis was 2% in the 1970s. Furthermore, Ae. serratus, a recently implicated vector of yellow fever virus in the State of Rio Grande do Sul, should be a target for the entomological surveillance in the southeastern Atlantic Forest. Considering the continental dimensions of Brazil and the inherent difficulties in sampling its vast area, the habitat suitability method used in the study can be an important tool for predicting the distribution of vectors of pathogens.

Cation Distribution and Local Order in Mixed Sodium Metaphosphate Glasses

Two structural properties in mixed alkali metal phosphate glasses that seem to be crucial to the development of the mixed ion effect in dc conductivity were systematically analyzed in Na mixed metaphosphates: the local order around the mobile species, and their distribution and mixing in the glass network. The set of glasses considered here, Na1-xMxPO3 with M = Li, Ag, K, Rb, and Cs and 0 <= x <= 1, encompass a broad degree of size mismatch between the mixed cation species. A comprehensive solid-state nuclear magnetic resonance study was carried out using P-31 MAS, Na-23 triple quantum MAS, Rb-87 QCPMG, P-31-Na-23 REDOR, Na-23-Li-7 and Li-7-Li-6 SEDOR, and Na-23 spin echo decay. It was observed that the arrangement of P atoms around Na in the mixed glasses was indistinguishable from that observed in the NaPO3 glass. However, systematic distortions in the local structure of the 0 environments around Na were observed, related to the presence of the second cation. The average Na-O distances show an expansion/compression When Na+ ions are replaced by cations with respectively smaller/bigger radii. The behavior of the nuclear electric quadrupole coupling. constants indicates that this expansion reduces the local symmetry, while the compression produces the opposite effect These effects become marginally small when the site mismatch between the cations is small, as in Na-Ag mixed glasses. The present study confirms the intimate mixing of cation species at the atomic scale, but clear deviations from random mixing were detected in systems with larger alkali metal ions (Cs-Na, K-Na, Rb-Na). In contrast, no deviations from the statistical ion mixture were found in the systems Ag-Na and Li-Na, where mixed cations are either of radii comparable to (Ag+) or smaller than (Li+) Na+. The set of results supports two fundamental structural features of the models proposed to explain the mixed ion effect: the. structural specificity of the sites occupied by each cation species and their mixing at the atomic scale.

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898], proposed a new generalized distribution (denoted here with the prefix 'Kw-G'(Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-Gdensity function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155-161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279-285] and Kw-Flexible Weibull [M. Bebbington, C. D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719-726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Renyi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

STATISTICAL TEST FOR GENOTYPE AND ENVIRONMENT CONTRIBUTION IN THE GENOTYPES x ENVIRONMENTS INTERACTION MATRIX

The objective of the present work was to propose a method for testing the contribution of each level of the factors in a genotypes x environments (GxE) interaction using multi-environment trials analyses by means of an F test. The study evaluated a data set, with twenty genotypes and thirty-four environments, in a block design with four replications. The sum of squares within rows (genotypes) and columns (environments) of the GxE matrix was simulated, generating 10000 experiments to verify the empirical distribution. Results indicate a noncentral chi-square distribution for rows and columns of the GxE interaction matrix, which was also verified by the Kolmogorov-Smirnov test and Q-Q plot. Application of the F test identified the genotypes and environments that contributed the most to the GxE interaction. In this way, geneticists can select good genotypes in their studies.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.