A robust approach to joint modeling of mean and scale covariance for longitudinal data

In this paper, we propose a multivariate t$t$ regression model with its mean and scale covariance modeled jointly for the analysis of longitudinal data. A modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. We present three distinct representations of the log-likelihood function of the model and study the associated properties. A computationally efficient Fisher scoring algorithm is developed for carrying out maximum likelihood estimation. The technique for the prediction of future responses in this context is also investigated. The implementation of the proposed methodology is illustrated through two real-life examples and extensive simulation studies.     

Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive designs are sometimes used in a phase III clinical trial with the goal of allocating a larger number of patients to the better treatment. In the present paper we use some adaptive designs in a two-treatment two-period crossover trial in the presence of possible carry-over effects, where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also investigate related inferential problems, for which related asymptotics are derived. The proposed procedure is compared with a possible competitor. Finally we use real data sets to illustrate the applicability of our proposed design.     

Some developments on the log-Dagum distribution

Skewed and fat-tailed distributions frequently occur in many applications. Models proposed to deal with skewness and kurtosis may be difficult to treat because the density function cannot usually be written in a closed form and the moments might not exist. The log-Dagum distribution is a flexible and simple model obtained by a logarithmic transformation of the Dagum random variable. In this paper, some characteristics of the model are illustrated and the estimation of the parameters is considered. An application is given with the purpose of modeling kurtosis and skewness that mark the financial return distribution.      

On sequential Monte Carlo sampling methods for Bayesian filtering

In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.     

Separating the Harmful Versus Beneficial Effects of Marital Disruptions on Children

Although a marital disruption can certainly be harmful for some children, it might be beneficial to other children. Analyses on how children are affected by marital disruptions typically capture the average estimated effects (or associations) of a disruption on an outcome. Thus, the harmful effects of the disruption on some children are being averaged with the neutral and beneficial effects on other children. This could mute the estimated effect, and it could prevent the detection of significant harmful (or beneficial) effects. Using achievement test scores and an index of behavioral problems in a first-difference framework, I find evidence for the standard approach having muted estimated effects and failing to detect significant effects when the same data produce significant isolated harmful effects.     

On several estimates to the precision parameter of Dirichlet process prior

The article presents careful comparisons among several empirical Bayes estimates to the precision parameter of Dirichlet process prior, with the setup of univariate observations and multigroup data. Specifically, the data are equipped with a two-stage compound sampling model, where the prior is assumed as a Dirichlet process that follows within a Bayesian nonparametric framework. The precision parameter α measures the strength of the prior belief and kinds of estimates are generated on the basis of observations, including the naive estimate, two calibrated naive estimates, and two different types of maximum likelihood estimates stemming from distinct distributions. We explore some theoretical properties and provide explicitly detailed comparisons among these estimates, in the perspectives of bias, variance, and mean squared error. Besides, we further present the corresponding calculation algorithms and numerical simulations to illustrate our theoretical achievements.     

Generalized Weighted Exponential Distribution

The new class of weighted exponential (WE) distributions obtained by Gupta and Kundu (2009) by implementing Azzalini's method to the exponential distribution. In this study, we generalize the WE distribution to a new class of generalized weighted exponential (GWE) distribution. Several statistical and reliability properties of this new class of distribution are obtained. Estimation and inference procedure for distribution parameters are investigated. Finally, we show that the proposed model can provide better fit than the recent class of weighted exponential by using two real data examples.     

Inference for Burr XII distribution under Type I progressive hybrid censoring

We consider estimation of unknown parameters of a Burr XII distribution based on progressively Type I hybrid censored data. The maximum likelihood estimates are obtained using an expectation maximization algorithm. Asymptotic interval estimates are constructed from the Fisher information matrix. We obtain Bayes estimates under the squared error loss function using the Lindley method and Metropolis–Hastings algorithm. The predictive estimates of censored observations are obtained and the corresponding prediction intervals are also constructed. We compare the performance of the different methods using simulations. Two real datasets have been analyzed for illustrative purposes.     

Queue Length Analysis of MAP/G/1 Queue Under D-Policy

Abstract

We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided.