Recommendations on the nature of the passenger response time distribution to be used in the MSC 1033 assembly time analysis based on data derived from sea trials

The passenger response time distributions adopted by the International Maritime Organisation (IMO)in their assessment of the assembly time for passanger ships involves two key assumptions. The first is that the response time distribution assumes the form of a uniform random distribution and the second concerns the actual response times. These two assumptions are core to the validity of the IMO analysis but are not based on real data, being the recommendations of an IMO committee. In this paper, response time data collected from assembly trials conducted at sea on a real passanger vessel using actual passangers are presented and discussed. Unlike the IMO specified response time distributions, the data collected from these trials displays a log-normal distribution, similar to that found in land based environments. Based on this data, response time distributions for use in the IMO assesmbly for the day and night scenarios are suggested

The Effect of Volume Shape Factor on the Crystal Size Distribution of Fragments due to Attrition

The effect of volume shape factor on crystal size distribution (CSD) is usually ignored to simplify the analysis of population balance equation. In the present work, the CSD of fragments generated from a mechanically stirred crystallizer as the result of attrition mechanism has been reported when the volume shape factor conforms to normal distribution. The physical model of GAHN and MERSMANN which relates the attrition resistance of a crystalline substances to its mechanical properties has been employed. The simulation of fragment size distribution was performed by Monte Carlo (MC) technique. The results are compared with those reported by GAHN and MERSMANN.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

A new study on the power distribution of OFDMA, SC-FDMA and CP-CDMA signals

This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function (PDF) solved numerically. The Complementary Cumulative Distribution Function (CCDF) of Instantaneous Power to Average Power Ratio (IPAPR) is computed from the structure of the transmit system matrix. This helps intuitively understand the distribution of output signal power if the structure of the transmit system matrix and the constellation used are known. The distribution obtained for OFDMA signal matches complex normal distribution. The results indicate why the CCDF of IPAPR in case of SC-FDMA is better than OFDMA for a given constellation. Finally, with this method it is shown again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR. The insight that this technique provides may be useful in designing area optimised digital and power efficient analogue modules.

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Measurement error models with a general class of error distribution

In general, the normal distribution is assumed for the surrogate of the true covariates in the classical error model. This paper considers a class of distributions, which includes the normal one, for the variables subject to error. An estimation approach yielding consistent estimators is developed and simulation studies reported.

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz`s Bayesian information criterion and Hannan-Quinn criterion.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Bayesian density estimation using Skew Student-t-Normal mixtures

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gomez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed. (c) 2008 Elsevier B.V. All rights reserved.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.