A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

A simple and effective inverse projection scheme for void distribution control in topology optimization

The ability to control both the minimum size of holes and the minimum size of structural members are essential requirements in the topology optimization design process for manufacturing. This paper addresses both requirements by means of a unified approach involving mesh-independent projection techniques. An inverse projection is developed to control the minimum hole size while a standard direct projection scheme is used to control the minimum length of structural members. In addition, a heuristic scheme combining both contrasting requirements simultaneously is discussed. Two topology optimization implementations are contributed: one in which the projection (either inverse or direct) is used at each iteration; and the other in which a two-phase scheme is explored. In the first phase, the compliance minimization is carried out without any projection until convergence. In the second phase, the chosen projection scheme is applied iteratively until a solution is obtained while satisfying either the minimum member size or minimum hole size. Examples demonstrate the various features of the projection-based techniques presented.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. 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.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

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.

Sequence and tissue distribution of chicken cellular nucleic acid binding protein cDNA

We sequenced cDNAs coding for chicken cellular nucleic acid binding protein (CNBP). Two slightly different variations of the open reading frame were found, each of which translates into a protein with seven zinc finger domains. The longest transcript contains an in-frame insert of 3 bp. The sequence conservation between chick CNBP cDNAs with human, rat and mouse CNBP cDNAs is extreme, especially in the coding region, where the deduced amino acid sequence identity with human, rat and mouse CNBP is 99%. CNBP-like transcripts were also found in various tissues from insect, shrimp, fish and lizard. Regions with remarkable nucleotide conservation were also found in the 3' untranslated region, indicating important functions for these regions. Quantitative reverse transcription polymerase chain reaction (RT-PCR) indicated that in the chick, CNBP is present in all tissues examined in approximately equal ratios to total RNA. RT-PCR of total RNA isolated from different phyla indicate CNBP-like proteins art widespread throughout the animal kingdom. The extraordinary level of conservation suggests an important physiological role for CNBP. (C) 1997 Elsevier Science Inc.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

The Fornax spectroscopic survey I. Survey strategy and preliminary results on the redshift distribution of a complete sample of stars and galaxies

The Fornax Spectroscopic Survey will use the Two degree Field spectrograph (2dF) of the Angle-Australian Telescope to obtain spectra for a complete sample of all 14000 objects with 16.5 less than or equal to b(j) less than or equal to 19.7 in a 12 square degree area centred on the Fornax Cluster. The aims of this project include the study of dwarf galaxies in the cluster (both known low surface brightness objects and putative normal surface brightness dwarfs) and a comparison sample of background field galaxies. We will also measure quasars and other active galaxies, any previously unrecognised compact galaxies and a large sample of Galactic stars. By selecting all objects-both stars and galaxies-independent of morphology, we cover a much larger range of surface brightness and scale size than previous surveys. In this paper we first describe the design of the survey. Our targets are selected from UK Schmidt Telescope sky survey plates digitised by the Automated Plate Measuring (APM) facility. We then describe the photometric and astrometric calibration of these data and show that the APM astrometry is accurate enough for use with the 2dF. We also describe a general approach to object identification using cross-correlations which allows us to identify and classify both stellar and galaxy spectra. We present results from the first 2dF field. Redshift distributions and velocity structures are shown for all observed objects in the direction of Fornax, including Galactic stars? galaxies in and around the Fornax Cluster, and for the background galaxy population. The velocity data for the stars show the contributions from the different Galactic components, plus a small tail to high velocities. We find no galaxies in the foreground to the cluster in our 2dF field. The Fornax Cluster is clearly defined kinematically. The mean velocity from the 26 cluster members having reliable redshifts is 1560 +/- 80 km s(-1). They show a velocity dispersion of 380 +/- 50 km s(-1). Large-scale structure can be traced behind the cluster to a redshift beyond z = 0.3. Background compact galaxies and low surface brightness galaxies are found to follow the general galaxy distribution.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

The large-scale distribution of neutral hydrogen in the Fornax region

Using data from the H I Parkes All Sky Survey (HIPASS), we have searched for neutral hydrogen in galaxies in a region similar to25x25 deg(2) centred on NGC 1399, the nominal centre of the Fornax cluster. Within a velocity search range of 300-3700 km s(-1) and to a 3sigma lower flux limit of similar to40 mJy, 110 galaxies with H I emission were detected, one of which is previously uncatalogued. None of the detections has early-type morphology. Previously unknown velocities for 14 galaxies have been determined, with a further four velocity measurements being significantly dissimilar to published values. Identification of an optical counterpart is relatively unambiguous for more than similar to90 per cent of our H I galaxies. The galaxies appear to be embedded in a sheet at the cluster velocity which extends for more than 30degrees across the search area. At the nominal cluster distance of similar to20 Mpc, this corresponds to an elongated structure more than 10 Mpc in extent. A velocity gradient across the structure is detected, with radial velocities increasing by similar to500 km s(-1) from south-east to north-west. The clustering of galaxies evident in optical surveys is only weakly suggested in the spatial distribution of our H I detections. Of 62 H I detections within a 10degrees projected radius of the cluster centre, only two are within the core region (projected radius

Modelling the Distribution of Ischaemic Stroke-Specific Survival Time Using an EM-based Mixture Approach with Random Effects Adjustment

A two-component survival mixture model is proposed to analyse a set of ischaemic stroke-specific mortality data. The survival experience of stroke patients after index stroke may be described by a subpopulation of patients in the acute condition and another subpopulation of patients in the chronic phase. To adjust for the inherent correlation of observations due to random hospital effects, a mixture model of two survival functions with random effects is formulated. Assuming a Weibull hazard in both components, an EM algorithm is developed for the estimation of fixed effect parameters and variance components. A simulation study is conducted to assess the performance of the two-component survival mixture model estimators. Simulation results confirm the applicability of the proposed model in a small sample setting. Copyright (C) 2004 John Wiley Sons, Ltd.